a positive-displacement blower feeding an aeration basin Given volumetric flow (Q) = 5.4000 m^3/s; pressure rise (\Delta p) = 18,400 Pa; efficiency (\eta) = 0.5800, 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) = 5.4000 m^3/s, pressure rise (\Delta p) = 18,400 Pa, efficiency (\eta) = 0.5800.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{5.4000 18400}{0.5800}$$

5. Step 5 — Evaluate:

   $$W = 171310\ \text{W}$$

6. Step 6 — Check: returning W = 171,310 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

• 342,621 — kept a factor of two that cancels in the correct rearrangement.
• 85,655 — dropped that same factor in the other direction.
• 188,441 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a centrifugal blower on a dust-collection duct Given shaft power (W) = 81,366 W; pressure rise (\Delta p) = 9,400 Pa; efficiency (\eta) = 0.6000, 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) = 81,366 W, pressure rise (\Delta p) = 9,400 Pa, efficiency (\eta) = 0.6000.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{81366 0.6000}{9400}$$

5. Step 5 — Evaluate:

   Q = 5.1936\ \text{m^3/s}

6. Step 6 — Check: returning Q = 5.1936 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

• 10.3871 — kept a factor of two that cancels in the correct rearrangement.
• 2.5968 — dropped that same factor in the other direction.
• 5.7129 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a compressor supplying pneumatic construction tools Given shaft power (W) = 184,681 W; volumetric flow (Q) = 3.7000 m^3/s; pressure rise (\Delta p) = 28,400 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) = 184,681 W, volumetric flow (Q) = 3.7000 m^3/s, pressure rise (\Delta p) = 28,400 Pa.

4. Step 4 — Substitute the given values:

   $$\eta = \dfrac{3.7000 28400}{184681}$$

5. Step 5 — Evaluate:

   $$\eta = 0.5690$$

6. Step 6 — Check: returning \eta = 0.5690 to

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

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

Why the other options are there

• 1.1380 — kept a factor of two that cancels in the correct rearrangement.
• 0.2845 — dropped that same factor in the other direction.
• 0.6259 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a positive-displacement blower feeding an aeration basin Given volumetric flow (Q) = 7.1000 m^3/s; pressure rise (\Delta p) = 40,700 Pa; efficiency (\eta) = 0.6400, 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) = 7.1000 m^3/s, pressure rise (\Delta p) = 40,700 Pa, efficiency (\eta) = 0.6400.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{7.1000 40700}{0.6400}$$

5. Step 5 — Evaluate:

   $$W = 451516\ \text{W}$$

6. Step 6 — Check: returning W = 451,516 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

• 903,031 — kept a factor of two that cancels in the correct rearrangement.
• 225,758 — dropped that same factor in the other direction.
• 496,667 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a centrifugal blower on a dust-collection duct Given shaft power (W) = 160,051 W; pressure rise (\Delta p) = 59,600 Pa; efficiency (\eta) = 0.7600, 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) = 160,051 W, pressure rise (\Delta p) = 59,600 Pa, efficiency (\eta) = 0.7600.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{160051 0.7600}{59600}$$

5. Step 5 — Evaluate:

   Q = 2.0409\ \text{m^3/s}

6. Step 6 — Check: returning Q = 2.0409 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

• 4.0818 — kept a factor of two that cancels in the correct rearrangement.
• 1.0205 — dropped that same factor in the other direction.
• 2.2450 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a compressor supplying pneumatic construction tools Given shaft power (W) = 24,108 W; volumetric flow (Q) = 1.4000 m^3/s; pressure rise (\Delta p) = 16,100 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) = 24,108 W, volumetric flow (Q) = 1.4000 m^3/s, pressure rise (\Delta p) = 16,100 Pa.

4. Step 4 — Substitute the given values:

   $$\eta = \dfrac{1.4000 16100}{24108}$$

5. Step 5 — Evaluate:

   $$\eta = 0.9350$$

6. Step 6 — Check: returning \eta = 0.9350 to

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

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

Why the other options are there

• 1.8699 — kept a factor of two that cancels in the correct rearrangement.
• 0.4675 — dropped that same factor in the other direction.
• 1.0285 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a positive-displacement blower feeding an aeration basin Given volumetric flow (Q) = 3.9000 m^3/s; pressure rise (\Delta p) = 18,400 Pa; efficiency (\eta) = 0.8500, 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) = 3.9000 m^3/s, pressure rise (\Delta p) = 18,400 Pa, efficiency (\eta) = 0.8500.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{3.9000 18400}{0.8500}$$

5. Step 5 — Evaluate:

   $$W = 84424\ \text{W}$$

6. Step 6 — Check: returning W = 84,424 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

• 168,847 — kept a factor of two that cancels in the correct rearrangement.
• 42,212 — dropped that same factor in the other direction.
• 92,866 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a centrifugal blower on a dust-collection duct Given shaft power (W) = 20,876 W; pressure rise (\Delta p) = 37,000 Pa; efficiency (\eta) = 0.8200, 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) = 20,876 W, pressure rise (\Delta p) = 37,000 Pa, efficiency (\eta) = 0.8200.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{20876 0.8200}{37000}$$

5. Step 5 — Evaluate:

   Q = 0.4627\ \text{m^3/s}

6. Step 6 — Check: returning Q = 0.4627 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

• 0.9253 — kept a factor of two that cancels in the correct rearrangement.
• 0.2313 — dropped that same factor in the other direction.
• 0.5089 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a compressor supplying pneumatic construction tools Given shaft power (W) = 49,868 W; volumetric flow (Q) = 4.4000 m^3/s; pressure rise (\Delta p) = 27,700 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) = 49,868 W, volumetric flow (Q) = 4.4000 m^3/s, pressure rise (\Delta p) = 27,700 Pa.

4. Step 4 — Substitute the given values:

   $$\eta = \dfrac{4.4000 27700}{49868}$$

5. Step 5 — Evaluate:

   $$\eta = 2.4441$$

6. Step 6 — Check: returning \eta = 2.4441 to

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

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

Why the other options are there

• 4.8881 — kept a factor of two that cancels in the correct rearrangement.
• 1.2220 — dropped that same factor in the other direction.
• 2.6885 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors

a positive-displacement blower feeding an aeration basin Given volumetric flow (Q) = 6.7000 m^3/s; pressure rise (\Delta p) = 56,300 Pa; efficiency (\eta) = 0.8200, 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) = 6.7000 m^3/s, pressure rise (\Delta p) = 56,300 Pa, efficiency (\eta) = 0.8200.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{6.7000 56300}{0.8200}$$

5. Step 5 — Evaluate:

   $$W = 460012\ \text{W}$$

6. Step 6 — Check: returning W = 460,012 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

• 920,024 — kept a factor of two that cancels in the correct rearrangement.
• 230,006 — dropped that same factor in the other direction.
• 506,013 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors