Net Positive Suction Head Available (NPSHA)

Example 1

Net Positive Suction Head Available (NPSHA) — solve for NPSH available — Net Positive Suction Head Available (NPSHA)

Net Positive Suction Head Available for a centrifugal pump drawing from a sump Given atmospheric pressure (p_atm) = 101,100 Pa; vapor pressure (p_v) = 2,350 Pa; specific weight (gamma) = 9,725 N/m^3; static suction lift (z_s) = 0.9000 m; suction pipe friction loss (h_fs) = 1.1500 m, determine the NPSH available (NPSHA) in m.

Given

$atmospheric pressure (p_atm) = 101,100 Pa$
$vapor pressure (p_v) = 2,350 Pa$
$specific weight (gamma) = 9,725 N/m^3$
$static suction lift (z_s) = 0.9000 m$
$suction pipe friction loss (h_fs) = 1.1500 m$

Find

NPSH available (NPSHA), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except NPSHA is given, so isolate NPSHA symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 1 — schematic for Net Positive Suction Head Available (NPSHA) — solve for NPSH available — Net Positive Suction Head Available (NPSHA)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that NPSHA stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 101,100 Pa, vapor pressure (p_v) = 2,350 Pa, specific weight (gamma) = 9,725 N/m^3, static suction lift (z_s) = 0.9000 m, suction pipe friction loss (h_fs) = 1.1500 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$NPSHA = 8.1042\ \text{m}$
Step 6 — Check: returning NPSHA = 8.1042 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

NPSHA = 8.1042\ \text{m}

Why the other options are there

16.2085 — kept a factor of two that cancels in the correct rearrangement.
4.0521 — dropped that same factor in the other direction.
8.9147 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 2

Net Positive Suction Head Available (NPSHA) — solve for static suction lift — Net Positive Suction Head Available (NPSHA) (2)

NPSHA calculation for a pump lifting water through a suction pipe Given atmospheric pressure (p_atm) = 100,100 Pa; vapor pressure (p_v) = 4,850 Pa; specific weight (gamma) = 9,710 N/m^3; suction pipe friction loss (h_fs) = 0.8000 m; NPSH available (NPSHA) = 3.2000 m, determine the static suction lift (z_s) in m.

Given

$atmospheric pressure (p_atm) = 100,100 Pa$
$vapor pressure (p_v) = 4,850 Pa$
$specific weight (gamma) = 9,710 N/m^3$
$suction pipe friction loss (h_fs) = 0.8000 m$
$NPSH available (NPSHA) = 3.2000 m$

Find

static suction lift (z_s), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except z_s is given, so isolate z_s symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 2 — schematic for Net Positive Suction Head Available (NPSHA) — solve for static suction lift — Net Positive Suction Head Available (NPSHA) (2)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that z_s stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 100,100 Pa, vapor pressure (p_v) = 4,850 Pa, specific weight (gamma) = 9,710 N/m^3, suction pipe friction loss (h_fs) = 0.8000 m, NPSH available (NPSHA) = 3.2000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$z_{s} = 5.8095\ \text{m}$
Step 6 — Check: returning z_s = 5.8095 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

z_{s} = 5.8095\ \text{m}

Why the other options are there

11.6189 — kept a factor of two that cancels in the correct rearrangement.
2.9047 — dropped that same factor in the other direction.
6.3904 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 3

Net Positive Suction Head Available (NPSHA) — solve for suction pipe friction loss — Net Positive Suction Head Available (NPSHA) (3)

NPSHA for a boiler feed pump with elevated suction lift Given atmospheric pressure (p_atm) = 99,500 Pa; vapor pressure (p_v) = 4,600 Pa; specific weight (gamma) = 9,750 N/m^3; static suction lift (z_s) = 0.0000 m; NPSH available (NPSHA) = 8.5000 m, determine the suction pipe friction loss (h_fs) in m.

Given

$atmospheric pressure (p_atm) = 99,500 Pa$
$vapor pressure (p_v) = 4,600 Pa$
$specific weight (gamma) = 9,750 N/m^3$
$static suction lift (z_s) = 0.0000 m$
$NPSH available (NPSHA) = 8.5000 m$

Find

suction pipe friction loss (h_fs), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except h_fs is given, so isolate h_fs symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 3 — schematic for Net Positive Suction Head Available (NPSHA) — solve for suction pipe friction loss — Net Positive Suction Head Available (NPSHA) (3)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that h_fs stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 99,500 Pa, vapor pressure (p_v) = 4,600 Pa, specific weight (gamma) = 9,750 N/m^3, static suction lift (z_s) = 0.0000 m, NPSH available (NPSHA) = 8.5000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$h_{fs} = 1.2333\ \text{m}$
Step 6 — Check: returning h_fs = 1.2333 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

h_{fs} = 1.2333\ \text{m}

Why the other options are there

2.4667 — kept a factor of two that cancels in the correct rearrangement.
0.6167 — dropped that same factor in the other direction.
1.3567 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 4

Net Positive Suction Head Available (NPSHA) — solve for NPSH available (case 2) — Net Positive Suction Head Available (NPSHA) (4)

Net Positive Suction Head Available for a centrifugal pump drawing from a sump Given atmospheric pressure (p_atm) = 97,200 Pa; vapor pressure (p_v) = 3,150 Pa; specific weight (gamma) = 9,745 N/m^3; static suction lift (z_s) = -2.5000 m; suction pipe friction loss (h_fs) = 1.2500 m, determine the NPSH available (NPSHA) in m.

Given

$atmospheric pressure (p_atm) = 97,200 Pa$
$vapor pressure (p_v) = 3,150 Pa$
$specific weight (gamma) = 9,745 N/m^3$
$static suction lift (z_s) = -2.5000 m$
$suction pipe friction loss (h_fs) = 1.2500 m$

Find

NPSH available (NPSHA), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except NPSHA is given, so isolate NPSHA symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 4 — schematic for Net Positive Suction Head Available (NPSHA) — solve for NPSH available (case 2) — Net Positive Suction Head Available (NPSHA) (4)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that NPSHA stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 97,200 Pa, vapor pressure (p_v) = 3,150 Pa, specific weight (gamma) = 9,745 N/m^3, static suction lift (z_s) = -2.5000 m, suction pipe friction loss (h_fs) = 1.2500 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$NPSHA = 10.9011\ \text{m}$
Step 6 — Check: returning NPSHA = 10.9011 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

NPSHA = 10.9011\ \text{m}

Why the other options are there

21.8022 — kept a factor of two that cancels in the correct rearrangement.
5.4506 — dropped that same factor in the other direction.
11.9912 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 5

Net Positive Suction Head Available (NPSHA) — solve for static suction lift (case 2) — Net Positive Suction Head Available (NPSHA) (5)

NPSHA calculation for a pump lifting water through a suction pipe Given atmospheric pressure (p_atm) = 95,400 Pa; vapor pressure (p_v) = 3,900 Pa; specific weight (gamma) = 9,810 N/m^3; suction pipe friction loss (h_fs) = 0.5000 m; NPSH available (NPSHA) = 3.4000 m, determine the static suction lift (z_s) in m.

Given

$atmospheric pressure (p_atm) = 95,400 Pa$
$vapor pressure (p_v) = 3,900 Pa$
$specific weight (gamma) = 9,810 N/m^3$
$suction pipe friction loss (h_fs) = 0.5000 m$
$NPSH available (NPSHA) = 3.4000 m$

Find

static suction lift (z_s), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except z_s is given, so isolate z_s symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 5 — schematic for Net Positive Suction Head Available (NPSHA) — solve for static suction lift (case 2) — Net Positive Suction Head Available (NPSHA) (5)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that z_s stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 95,400 Pa, vapor pressure (p_v) = 3,900 Pa, specific weight (gamma) = 9,810 N/m^3, suction pipe friction loss (h_fs) = 0.5000 m, NPSH available (NPSHA) = 3.4000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$z_{s} = 5.4272\ \text{m}$
Step 6 — Check: returning z_s = 5.4272 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

z_{s} = 5.4272\ \text{m}

Why the other options are there

10.8544 — kept a factor of two that cancels in the correct rearrangement.
2.7136 — dropped that same factor in the other direction.
5.9699 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 6

Net Positive Suction Head Available (NPSHA) — solve for suction pipe friction loss (case 2) — Net Positive Suction Head Available (NPSHA) (6)

NPSHA for a boiler feed pump with elevated suction lift Given atmospheric pressure (p_atm) = 100,500 Pa; vapor pressure (p_v) = 2,900 Pa; specific weight (gamma) = 9,755 N/m^3; static suction lift (z_s) = 0.4000 m; NPSH available (NPSHA) = 11.0000 m, determine the suction pipe friction loss (h_fs) in m.

Given

$atmospheric pressure (p_atm) = 100,500 Pa$
$vapor pressure (p_v) = 2,900 Pa$
$specific weight (gamma) = 9,755 N/m^3$
$static suction lift (z_s) = 0.4000 m$
$NPSH available (NPSHA) = 11.0000 m$

Find

suction pipe friction loss (h_fs), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except h_fs is given, so isolate h_fs symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 6 — schematic for Net Positive Suction Head Available (NPSHA) — solve for suction pipe friction loss (case 2) — Net Positive Suction Head Available (NPSHA) (6)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that h_fs stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 100,500 Pa, vapor pressure (p_v) = 2,900 Pa, specific weight (gamma) = 9,755 N/m^3, static suction lift (z_s) = 0.4000 m, NPSH available (NPSHA) = 11.0000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$h_{fs} = -1.3949\ \text{m}$
Step 6 — Check: returning h_fs = -1.3949 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

h_{fs} = -1.3949\ \text{m}

Why the other options are there

-2.7897 — kept a factor of two that cancels in the correct rearrangement.
-0.6974 — dropped that same factor in the other direction.
-1.5344 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 7

Net Positive Suction Head Available (NPSHA) — solve for NPSH available (case 3) — Net Positive Suction Head Available (NPSHA) (7)

Net Positive Suction Head Available for a centrifugal pump drawing from a sump Given atmospheric pressure (p_atm) = 96,800 Pa; vapor pressure (p_v) = 3,550 Pa; specific weight (gamma) = 9,780 N/m^3; static suction lift (z_s) = 0.1000 m; suction pipe friction loss (h_fs) = 1.2000 m, determine the NPSH available (NPSHA) in m.

Given

$atmospheric pressure (p_atm) = 96,800 Pa$
$vapor pressure (p_v) = 3,550 Pa$
$specific weight (gamma) = 9,780 N/m^3$
$static suction lift (z_s) = 0.1000 m$
$suction pipe friction loss (h_fs) = 1.2000 m$

Find

NPSH available (NPSHA), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except NPSHA is given, so isolate NPSHA symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 7 — schematic for Net Positive Suction Head Available (NPSHA) — solve for NPSH available (case 3) — Net Positive Suction Head Available (NPSHA) (7)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that NPSHA stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 96,800 Pa, vapor pressure (p_v) = 3,550 Pa, specific weight (gamma) = 9,780 N/m^3, static suction lift (z_s) = 0.1000 m, suction pipe friction loss (h_fs) = 1.2000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$NPSHA = 8.2348\ \text{m}$
Step 6 — Check: returning NPSHA = 8.2348 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

NPSHA = 8.2348\ \text{m}

Why the other options are there

16.4695 — kept a factor of two that cancels in the correct rearrangement.
4.1174 — dropped that same factor in the other direction.
9.0582 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 8

Net Positive Suction Head Available (NPSHA) — solve for static suction lift (case 3) — Net Positive Suction Head Available (NPSHA) (8)

NPSHA calculation for a pump lifting water through a suction pipe Given atmospheric pressure (p_atm) = 99,400 Pa; vapor pressure (p_v) = 1,850 Pa; specific weight (gamma) = 9,725 N/m^3; suction pipe friction loss (h_fs) = 0.7500 m; NPSH available (NPSHA) = 2.0000 m, determine the static suction lift (z_s) in m.

Given

$atmospheric pressure (p_atm) = 99,400 Pa$
$vapor pressure (p_v) = 1,850 Pa$
$specific weight (gamma) = 9,725 N/m^3$
$suction pipe friction loss (h_fs) = 0.7500 m$
$NPSH available (NPSHA) = 2.0000 m$

Find

static suction lift (z_s), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except z_s is given, so isolate z_s symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 8 — schematic for Net Positive Suction Head Available (NPSHA) — solve for static suction lift (case 3) — Net Positive Suction Head Available (NPSHA) (8)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that z_s stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 99,400 Pa, vapor pressure (p_v) = 1,850 Pa, specific weight (gamma) = 9,725 N/m^3, suction pipe friction loss (h_fs) = 0.7500 m, NPSH available (NPSHA) = 2.0000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$z_{s} = 7.2808\ \text{m}$
Step 6 — Check: returning z_s = 7.2808 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

z_{s} = 7.2808\ \text{m}

Why the other options are there

14.5617 — kept a factor of two that cancels in the correct rearrangement.
3.6404 — dropped that same factor in the other direction.
8.0089 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 9

Net Positive Suction Head Available (NPSHA) — solve for suction pipe friction loss (case 3) — Net Positive Suction Head Available (NPSHA) (9)

NPSHA for a boiler feed pump with elevated suction lift Given atmospheric pressure (p_atm) = 95,700 Pa; vapor pressure (p_v) = 1,800 Pa; specific weight (gamma) = 9,710 N/m^3; static suction lift (z_s) = -1.1000 m; NPSH available (NPSHA) = 9.0000 m, determine the suction pipe friction loss (h_fs) in m.

Given

$atmospheric pressure (p_atm) = 95,700 Pa$
$vapor pressure (p_v) = 1,800 Pa$
$specific weight (gamma) = 9,710 N/m^3$
$static suction lift (z_s) = -1.1000 m$
$NPSH available (NPSHA) = 9.0000 m$

Find

suction pipe friction loss (h_fs), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except h_fs is given, so isolate h_fs symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 9 — schematic for Net Positive Suction Head Available (NPSHA) — solve for suction pipe friction loss (case 3) — Net Positive Suction Head Available (NPSHA) (9)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that h_fs stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 95,700 Pa, vapor pressure (p_v) = 1,800 Pa, specific weight (gamma) = 9,710 N/m^3, static suction lift (z_s) = -1.1000 m, NPSH available (NPSHA) = 9.0000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$h_{fs} = 1.7704\ \text{m}$
Step 6 — Check: returning h_fs = 1.7704 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

h_{fs} = 1.7704\ \text{m}

Why the other options are there

3.5409 — kept a factor of two that cancels in the correct rearrangement.
0.8852 — dropped that same factor in the other direction.
1.9475 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Example 10

Net Positive Suction Head Available (NPSHA) — solve for NPSH available (case 4) — Net Positive Suction Head Available (NPSHA) (10)

Net Positive Suction Head Available for a centrifugal pump drawing from a sump Given atmospheric pressure (p_atm) = 96,700 Pa; vapor pressure (p_v) = 4,400 Pa; specific weight (gamma) = 9,720 N/m^3; static suction lift (z_s) = 3.0000 m; suction pipe friction loss (h_fs) = 1.5000 m, determine the NPSH available (NPSHA) in m.

Given

$atmospheric pressure (p_atm) = 96,700 Pa$
$vapor pressure (p_v) = 4,400 Pa$
$specific weight (gamma) = 9,720 N/m^3$
$static suction lift (z_s) = 3.0000 m$
$suction pipe friction loss (h_fs) = 1.5000 m$

Find

NPSH available (NPSHA), in m

Start with the thinking

The governing relation printed in this handbook section is Net Positive Suction Head Available (NPSHA).
Everything except NPSHA is given, so isolate NPSHA symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Net Positive Suction Head Available (NPSHA) checks whether a pump's suction pipe will cavitate.

Figure 10 — schematic for Net Positive Suction Head Available (NPSHA) — solve for NPSH available (case 4) — Net Positive Suction Head Available (NPSHA) (10)

Step-by-step solution

Step 1 — State the governing relation:
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
Step 2 — Rearrange the relation so that NPSHA stands alone on the left-hand side.
Step 3 — List the givens: atmospheric pressure (p_atm) = 96,700 Pa, vapor pressure (p_v) = 4,400 Pa, specific weight (gamma) = 9,720 N/m^3, static suction lift (z_s) = 3.0000 m, suction pipe friction loss (h_fs) = 1.5000 m.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$NPSHA = 4.9959\ \text{m}$
Step 6 — Check: returning NPSHA = 4.9959 m to
$NPSHA = \dfrac{p_atm}{\gamma} - \dfrac{p_v}{\gamma} \pm z_s - h_{f,s}$
reproduces the given quantities, and both sides carry the same units.

Answer:

NPSHA = 4.9959\ \text{m}

Why the other options are there

9.9918 — kept a factor of two that cancels in the correct rearrangement.
2.4979 — dropped that same factor in the other direction.
5.4955 — rounded an intermediate value before the final step.

Reference: FE Handbook — Net Positive Suction Head Available (NPSHA)

Net Positive Suction Head Available (NPSHA)

Core formulas for this FE topic

Worked exam-style examples

Net Positive Suction Head Available (NPSHA)

Core formulas for this FE topic

NPSHA=Hpa+Hs−/hL−Hvp=tinletNPSHA = Hpa + Hs - / hL - Hvp = tinletNPSHA=Hpa+Hs−/hL−Hvp=tinlet

Hpa=atmosphericpressureheadonthesurfaceoftheliquidinthesump(ftorm)Hpa = atmospheric pressure head on the surface of the liquid in the sump (ft or m)Hpa=atmosphericpressureheadonthesurfaceoftheliquidinthesump(ftorm)

ΣhL = total friction losses in the suction line (ft or m)Needs technical review

Hvp=vaporpressureheadoftheliquidattheoperatingtemperature(ftorm)Hvp = vapor pressure head of the liquid at the operating temperature (ft or m)Hvp=vaporpressureheadoftheliquidattheoperatingtemperature(ftorm)

v=fluidvelocityatpumpinletv = fluid velocity at pump inletv=fluidvelocityatpumpinlet

Pvapor=fluidvaporpressureatpumpinletPvapor = fluid vapor pressure at pump inletPvapor=fluidvaporpressureatpumpinlet

ρ=fluiddensity\rho = fluid densityρ=fluiddensity

g=accelerationduetogravityg = acceleration due to gravityg=accelerationduetogravity

FluidpowerWofluid=tgHQFluid power Wofluid = tgHQFluidpowerWofluid=tgHQ

PumpbrakehpowerWo=hPump ^brake h power Wo = hPumpbrakehpowerWo=h

PurchasedpowerWopurchased=hmotorPurchased power Wopurchased = hmotorPurchasedpowerWopurchased=hmotor

ηpump = pump efficiency ^0 to 1 hNeeds technical review

ηmotor = motor efficiency ^0 to 1 hNeeds technical review

H=headincreaseprovidedbypumpH = head increase provided by pumpH=headincreaseprovidedbypump

Worked exam-style examples