Characteristics of a Static Liquid

Fluid Mechanics · FE Reference Handbook section

Fluid Mechanics

3 formulas

10 exam-style examples

~51 min

All Fluid Mechanics lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

The Pressure Field in a Static Liquid
The difference in pressure between two different points is
Bober, W., and R.A. Kenyon, Fluid Mechanics, Wiley, 1980. Diagrams reprinted by permission of William Bober and Richard A. Kenyon.

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1

Hydrostatic pressure at depth — Characteristics of a Static Liquid

Find the gauge pressure 9.0 ft below the surface of a fluid with specific gravity 0.80.

Given

$h = 9.0 ft$
$SG = 0.80$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 1 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 0.80(62.4) = 49.92 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 49.92(9.0) = 449.3 psf$
Convert
$p = 449.3/144 = 3.12 psi$

Answer:

p ≈ 449.3 psf (3.12 psi)

Why the other options are there

561.6 psf (specific gravity ignored)
64,696 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 2

Hydrostatic pressure at depth — Characteristics of a Static Liquid (2)

Find the gauge pressure 7.0 ft below the surface of a fluid with specific gravity 1.80.

Given

$h = 7.0 ft$
$SG = 1.80$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 2 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (2)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 1.80(62.4) = 112.3 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 112.3(7.0) = 786.2 psf$
Convert
$p = 786.2/144 = 5.46 psi$

Answer:

p ≈ 786.2 psf (5.46 psi)

Why the other options are there

436.8 psf (specific gravity ignored)
113,219 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 3

Hydrostatic pressure at depth — Characteristics of a Static Liquid (3)

Find the gauge pressure 13.0 ft below the surface of a fluid with specific gravity 4.40.

Given

$h = 13.0 ft$
$SG = 4.40$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 3 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (3)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 4.40(62.4) = 274.6 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 274.6(13.0) = 3,569 psf$
Convert
$p = 3,569/144 = 24.79 psi$

Answer:

p ≈ 3,569 psf (24.79 psi)

Why the other options are there

811.2 psf (specific gravity ignored)
513,976 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 4

Hydrostatic pressure at depth — Characteristics of a Static Liquid (4)

Find the gauge pressure 17.5 ft below the surface of a fluid with specific gravity 11.70.

Given

$h = 17.5 ft$
$SG = 11.70$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 4 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (4)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 11.70(62.4) = 730.1 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 730.1(17.5) = 12,776 psf$
Convert
$p = 12,776/144 = 88.72 psi$

Answer:

p ≈ 12,776 psf (88.72 psi)

Why the other options are there

1,092 psf (specific gravity ignored)
1,839,802 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 5

Hydrostatic pressure at depth — Characteristics of a Static Liquid (5)

Find the gauge pressure 23.0 ft below the surface of a fluid with specific gravity 12.90.

Given

$h = 23.0 ft$
$SG = 12.90$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 5 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (5)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 12.90(62.4) = 805.0 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 805.0(23.0) = 18,514 psf$
Convert
$p = 18,514/144 = 128.6 psi$

Answer:

p ≈ 18,514 psf (128.6 psi)

Why the other options are there

1,435 psf (specific gravity ignored)
2,666,028 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 6

Hydrostatic pressure at depth — Characteristics of a Static Liquid (6)

Find the gauge pressure 4.5 ft below the surface of a fluid with specific gravity 3.90.

Given

$h = 4.5 ft$
$SG = 3.90$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 6 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (6)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 3.90(62.4) = 243.4 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 243.4(4.5) = 1,095 psf$
Convert
$p = 1,095/144 = 7.60 psi$

Answer:

p ≈ 1,095 psf (7.60 psi)

Why the other options are there

280.8 psf (specific gravity ignored)
157,697 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 7

Hydrostatic pressure at depth — Characteristics of a Static Liquid (7)

Find the gauge pressure 11.5 ft below the surface of a fluid with specific gravity 10.50.

Given

$h = 11.5 ft$
$SG = 10.50$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 7 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (7)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 10.50(62.4) = 655.2 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 655.2(11.5) = 7,535 psf$
Convert
$p = 7,535/144 = 52.32 psi$

Answer:

p ≈ 7,535 psf (52.32 psi)

Why the other options are there

717.6 psf (specific gravity ignored)
1,085,011 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 8

Hydrostatic pressure at depth — Characteristics of a Static Liquid (8)

Find the gauge pressure 12.0 ft below the surface of a fluid with specific gravity 2.20.

Given

$h = 12.0 ft$
$SG = 2.20$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 8 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (8)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 2.20(62.4) = 137.3 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 137.3(12.0) = 1,647 psf$
Convert
$p = 1,647/144 = 11.44 psi$

Answer:

p ≈ 1,647 psf (11.44 psi)

Why the other options are there

748.8 psf (specific gravity ignored)
237,220 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 9

Hydrostatic pressure at depth — Characteristics of a Static Liquid (9)

Find the gauge pressure 26.0 ft below the surface of a fluid with specific gravity 13.20.

Given

$h = 26.0 ft$
$SG = 13.20$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 9 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (9)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 13.20(62.4) = 823.7 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 823.7(26.0) = 21,416 psf$
Convert
$p = 21,416/144 = 148.7 psi$

Answer:

p ≈ 21,416 psf (148.7 psi)

Why the other options are there

1,622 psf (specific gravity ignored)
3,083,858 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid

Example 10

Hydrostatic pressure at depth — Characteristics of a Static Liquid (10)

Find the gauge pressure 27.5 ft below the surface of a fluid with specific gravity 5.70.

Given

$h = 27.5 ft$
$SG = 5.70$
$\gamma_water = 62.4 lb/ft^{3}$

Find

Gauge pressure in psf and psi

Start with the thinking

Pressure grows linearly with depth, independent of container shape.
Specific weight = SG × 62.4.

Figure 10 — schematic for Hydrostatic pressure at depth — Characteristics of a Static Liquid (10)

Step-by-step solution

Specific weight
$\gamma = SG \times \gamma_w = 5.70(62.4) = 355.7 lb/ft^{3}$
Hydrostatic — p = γh
Substituting
$p = 355.7(27.5) = 9,781 psf$
Convert
$p = 9,781/144 = 67.93 psi$

Answer:

p ≈ 9,781 psf (67.93 psi)

Why the other options are there

1,716 psf (specific gravity ignored)
1,408,493 psf (conversion applied backwards)

Reference: FE Reference Handbook — Fluid Mechanics → Characteristics of a Static Liquid