blowers used for aeration in a wastewater basin Given weight flow rate (w) = 1.5000 N/s; actual inlet temperature ratio factor (Q) = 1.0000; discharge pressure (p_2) = 227.0 kPa; inlet pressure (p_1) = 97.0000 kPa; efficiency (e) = 0.6100, determine the blower power (P) in kW.

Start with the thinking

• The governing relation printed in this handbook section is Blowers (adiabatic power).
• Everything except P is given, so isolate P 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.
• Blowers deliver air at modest pressure rise, and their power is estimated from an adiabatic compression relation.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3 — List the givens: weight flow rate (w) = 1.5000 N/s, actual inlet temperature ratio factor (Q) = 1.0000, discharge pressure (p_2) = 227.0 kPa, inlet pressure (p_1) = 97.0000 kPa, efficiency (e) = 0.6100.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 0.0225\ \text{kW}$$

6. Step 6 — Check: returning P = 0.0225 kW to

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.0450 — kept a factor of two that cancels in the correct rearrangement.
• 0.0113 — dropped that same factor in the other direction.
• 0.0248 — rounded an intermediate value before the final step.

Reference: FE Handbook — Blowers

a centrifugal blower on a dust-collection duct Given volumetric flow (Q) = 8.8000 m^3/s; pressure rise (\Delta p) = 22,500 Pa; efficiency (\eta) = 0.5900, determine the shaft power (W) in W.

Start with the thinking

• The governing relation printed in this handbook section is Blower / compressor fluid power.
• Everything except W is given, so isolate W 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.
• A blower raises the pressure of an air stream across an aeration basin diffuser system.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \dfrac{Q \Delta p}{\eta}$$

2. Step 2 — Rearrange symbolically for W:

   $$W = \dfrac{Q \Delta p}{\eta}$$

3. Step 3 — List the givens: volumetric flow (Q) = 8.8000 m^3/s, pressure rise (\Delta p) = 22,500 Pa, efficiency (\eta) = 0.5900.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{8.8000 22500}{0.5900}$$

5. Step 5 — Evaluate:

   $$W = 335593\ \text{W}$$

6. Step 6 — Check: returning W = 335,593 W to

   $$W = \dfrac{Q \Delta p}{\eta}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 671,186 — kept a factor of two that cancels in the correct rearrangement.
• 167,797 — dropped that same factor in the other direction.
• 369,153 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

blowers supplying combustion air at low pressure rise Given weight flow rate (w) = 12.5000 N/s; actual inlet temperature ratio factor (Q) = 1.0000; discharge pressure (p_2) = 164.0 kPa; inlet pressure (p_1) = 97.5000 kPa; blower power (P) = 104.0 kW, determine the efficiency (e).

Start with the thinking

• The governing relation printed in this handbook section is Blowers (adiabatic power).
• Everything except e is given, so isolate e 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.
• Blowers deliver air at modest pressure rise, and their power is estimated from an adiabatic compression relation.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3 — List the givens: weight flow rate (w) = 12.5000 N/s, actual inlet temperature ratio factor (Q) = 1.0000, discharge pressure (p_2) = 164.0 kPa, inlet pressure (p_1) = 97.5000 kPa, blower power (P) = 104.0 kW.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 0.0006$$

6. Step 6 — Check: returning e = 0.0006 to

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.0013 — kept a factor of two that cancels in the correct rearrangement.
• 0.0003 — dropped that same factor in the other direction.
• 0.0007 — rounded an intermediate value before the final step.

Reference: FE Handbook — Blowers

a compressor supplying pneumatic construction tools Given shaft power (W) = 176,326 W; pressure rise (\Delta p) = 38,800 Pa; efficiency (\eta) = 0.6900, determine the volumetric flow (Q) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Blower / compressor fluid power.
• Everything except Q is given, so isolate Q 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.
• A blower raises the pressure of an air stream across an aeration basin diffuser system.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \dfrac{Q \Delta p}{\eta}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = \dfrac{W \eta}{\Delta p}$$

3. Step 3 — List the givens: shaft power (W) = 176,326 W, pressure rise (\Delta p) = 38,800 Pa, efficiency (\eta) = 0.6900.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{176326 0.6900}{38800}$$

5. Step 5 — Evaluate:

   Q = 3.1357\ \text{m^3/s}

6. Step 6 — Check: returning Q = 3.1357 m^3/s to

   $$W = \dfrac{Q \Delta p}{\eta}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 6.2714 — kept a factor of two that cancels in the correct rearrangement.
• 1.5678 — dropped that same factor in the other direction.
• 3.4493 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

blowers moving air through ductwork at elevated pressure Given weight flow rate (w) = 4.0000 N/s; actual inlet temperature ratio factor (Q) = 1.0000; discharge pressure (p_2) = 195.0 kPa; inlet pressure (p_1) = 95.5000 kPa; efficiency (e) = 0.8700, determine the blower power (P) in kW.

Start with the thinking

• The governing relation printed in this handbook section is Blowers (adiabatic power).
• Everything except P is given, so isolate P 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.
• Blowers deliver air at modest pressure rise, and their power is estimated from an adiabatic compression relation.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3 — List the givens: weight flow rate (w) = 4.0000 N/s, actual inlet temperature ratio factor (Q) = 1.0000, discharge pressure (p_2) = 195.0 kPa, inlet pressure (p_1) = 95.5000 kPa, efficiency (e) = 0.8700.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 0.0347\ \text{kW}$$

6. Step 6 — Check: returning P = 0.0347 kW to

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.0693 — kept a factor of two that cancels in the correct rearrangement.
• 0.0173 — dropped that same factor in the other direction.
• 0.0381 — rounded an intermediate value before the final step.

Reference: FE Handbook — Blowers

a positive-displacement blower feeding an aeration basin Given shaft power (W) = 102,017 W; volumetric flow (Q) = 10.4000 m^3/s; pressure rise (\Delta p) = 20,500 Pa, determine the efficiency (\eta).

Start with the thinking

• The governing relation printed in this handbook section is Blower / compressor fluid power.
• Everything except \eta is given, so isolate \eta 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.
• A blower raises the pressure of an air stream across an aeration basin diffuser system.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \dfrac{Q \Delta p}{\eta}$$

2. Step 2 — Rearrange symbolically for \eta:

   $$\eta = \dfrac{Q \Delta p}{W}$$

3. Step 3 — List the givens: shaft power (W) = 102,017 W, volumetric flow (Q) = 10.4000 m^3/s, pressure rise (\Delta p) = 20,500 Pa.

4. Step 4 — Substitute the given values:

   $$\eta = \dfrac{10.4000 20500}{102017}$$

5. Step 5 — Evaluate:

   $$\eta = 2.0898$$

6. Step 6 — Check: returning \eta = 2.0898 to

   $$W = \dfrac{Q \Delta p}{\eta}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 4.1797 — kept a factor of two that cancels in the correct rearrangement.
• 1.0449 — dropped that same factor in the other direction.
• 2.2988 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

blowers used for aeration in a wastewater basin Given weight flow rate (w) = 19.0000 N/s; actual inlet temperature ratio factor (Q) = 1.0000; discharge pressure (p_2) = 162.0 kPa; inlet pressure (p_1) = 97.0000 kPa; blower power (P) = 174.0 kW, determine the efficiency (e).

Start with the thinking

• The governing relation printed in this handbook section is Blowers (adiabatic power).
• Everything except e is given, so isolate e 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.
• Blowers deliver air at modest pressure rise, and their power is estimated from an adiabatic compression relation.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

2. Step 2 — Rearrange the relation so that e stands alone on the left-hand side.

3. Step 3 — List the givens: weight flow rate (w) = 19.0000 N/s, actual inlet temperature ratio factor (Q) = 1.0000, discharge pressure (p_2) = 162.0 kPa, inlet pressure (p_1) = 97.0000 kPa, blower power (P) = 174.0 kW.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$e = 0.0006$$

6. Step 6 — Check: returning e = 0.0006 to

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.0011 — kept a factor of two that cancels in the correct rearrangement.
• 0.0003 — dropped that same factor in the other direction.
• 0.0006 — rounded an intermediate value before the final step.

Reference: FE Handbook — Blowers

a centrifugal blower on a dust-collection duct Given volumetric flow (Q) = 3.8000 m^3/s; pressure rise (\Delta p) = 34,200 Pa; efficiency (\eta) = 0.6000, determine the shaft power (W) in W.

Start with the thinking

• The governing relation printed in this handbook section is Blower / compressor fluid power.
• Everything except W is given, so isolate W 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.
• A blower raises the pressure of an air stream across an aeration basin diffuser system.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \dfrac{Q \Delta p}{\eta}$$

2. Step 2 — Rearrange symbolically for W:

   $$W = \dfrac{Q \Delta p}{\eta}$$

3. Step 3 — List the givens: volumetric flow (Q) = 3.8000 m^3/s, pressure rise (\Delta p) = 34,200 Pa, efficiency (\eta) = 0.6000.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{3.8000 34200}{0.6000}$$

5. Step 5 — Evaluate:

   $$W = 216600\ \text{W}$$

6. Step 6 — Check: returning W = 216,600 W to

   $$W = \dfrac{Q \Delta p}{\eta}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 433,200 — kept a factor of two that cancels in the correct rearrangement.
• 108,300 — dropped that same factor in the other direction.
• 238,260 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

blowers supplying combustion air at low pressure rise Given weight flow rate (w) = 8.5000 N/s; actual inlet temperature ratio factor (Q) = 1.0000; discharge pressure (p_2) = 192.0 kPa; inlet pressure (p_1) = 98.5000 kPa; efficiency (e) = 0.7800, determine the blower power (P) in kW.

Start with the thinking

• The governing relation printed in this handbook section is Blowers (adiabatic power).
• Everything except P is given, so isolate P 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.
• Blowers deliver air at modest pressure rise, and their power is estimated from an adiabatic compression relation.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3 — List the givens: weight flow rate (w) = 8.5000 N/s, actual inlet temperature ratio factor (Q) = 1.0000, discharge pressure (p_2) = 192.0 kPa, inlet pressure (p_1) = 98.5000 kPa, efficiency (e) = 0.7800.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 0.0763\ \text{kW}$$

6. Step 6 — Check: returning P = 0.0763 kW to

   $$P = \dfrac{w Q}{29.7 e} \left[ \left(\dfrac{p_2}{p_1}\right)^{0.283} - 1 \right]$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.1526 — kept a factor of two that cancels in the correct rearrangement.
• 0.0381 — dropped that same factor in the other direction.
• 0.0839 — rounded an intermediate value before the final step.

Reference: FE Handbook — Blowers

a compressor supplying pneumatic construction tools Given shaft power (W) = 181,731 W; pressure rise (\Delta p) = 16,700 Pa; efficiency (\eta) = 0.8100, determine the volumetric flow (Q) in m^3/s.

Start with the thinking

• The governing relation printed in this handbook section is Blower / compressor fluid power.
• Everything except Q is given, so isolate Q 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.
• A blower raises the pressure of an air stream across an aeration basin diffuser system.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$W = \dfrac{Q \Delta p}{\eta}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = \dfrac{W \eta}{\Delta p}$$

3. Step 3 — List the givens: shaft power (W) = 181,731 W, pressure rise (\Delta p) = 16,700 Pa, efficiency (\eta) = 0.8100.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{181731 0.8100}{16700}$$

5. Step 5 — Evaluate:

   Q = 8.8145\ \text{m^3/s}

6. Step 6 — Check: returning Q = 8.8145 m^3/s to

   $$W = \dfrac{Q \Delta p}{\eta}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 17.6290 — kept a factor of two that cancels in the correct rearrangement.
• 4.4072 — dropped that same factor in the other direction.
• 9.6959 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors