a positive-displacement blower feeding an aeration basin Given volumetric flow (Q) = 11.5000 m^3/s; pressure rise (\Delta p) = 24,800 Pa; efficiency (\eta) = 0.7700, 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) = 11.5000 m^3/s, pressure rise (\Delta p) = 24,800 Pa, efficiency (\eta) = 0.7700.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{11.5000 24800}{0.7700}$$

5. Step 5 — Evaluate:

   $$W = 370390\ \text{W}$$

6. Step 6 — Check: returning W = 370,390 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

• 740,779 — kept a factor of two that cancels in the correct rearrangement.
• 185,195 — dropped that same factor in the other direction.
• 407,429 — 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) = 104,739 W; pressure rise (\Delta p) = 44,000 Pa; efficiency (\eta) = 0.6800, 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) = 104,739 W, pressure rise (\Delta p) = 44,000 Pa, efficiency (\eta) = 0.6800.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{104739 0.6800}{44000}$$

5. Step 5 — Evaluate:

   Q = 1.6187\ \text{m^3/s}

6. Step 6 — Check: returning Q = 1.6187 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

• 3.2374 — kept a factor of two that cancels in the correct rearrangement.
• 0.8093 — dropped that same factor in the other direction.
• 1.7806 — 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) = 83,942 W; volumetric flow (Q) = 0.4000 m^3/s; pressure rise (\Delta p) = 57,700 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) = 83,942 W, volumetric flow (Q) = 0.4000 m^3/s, pressure rise (\Delta p) = 57,700 Pa.

4. Step 4 — Substitute the given values:

   $$\eta = \dfrac{0.4000 57700}{83942}$$

5. Step 5 — Evaluate:

   $$\eta = 0.2750$$

6. Step 6 — Check: returning \eta = 0.2750 to

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

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

Why the other options are there

• 0.5499 — kept a factor of two that cancels in the correct rearrangement.
• 0.1375 — dropped that same factor in the other direction.
• 0.3024 — 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) = 8.1000 m^3/s; pressure rise (\Delta p) = 46,700 Pa; efficiency (\eta) = 0.5600, 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) = 8.1000 m^3/s, pressure rise (\Delta p) = 46,700 Pa, efficiency (\eta) = 0.5600.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{8.1000 46700}{0.5600}$$

5. Step 5 — Evaluate:

   $$W = 675482\ \text{W}$$

6. Step 6 — Check: returning W = 675,482 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

• 1,350,964 — kept a factor of two that cancels in the correct rearrangement.
• 337,741 — dropped that same factor in the other direction.
• 743,030 — 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) = 29,393 W; pressure rise (\Delta p) = 16,300 Pa; efficiency (\eta) = 0.6300, 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) = 29,393 W, pressure rise (\Delta p) = 16,300 Pa, efficiency (\eta) = 0.6300.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{29393 0.6300}{16300}$$

5. Step 5 — Evaluate:

   Q = 1.1360\ \text{m^3/s}

6. Step 6 — Check: returning Q = 1.1360 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

• 2.2721 — kept a factor of two that cancels in the correct rearrangement.
• 0.5680 — dropped that same factor in the other direction.
• 1.2497 — 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) = 138,164 W; volumetric flow (Q) = 5.5000 m^3/s; pressure rise (\Delta p) = 34,000 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) = 138,164 W, volumetric flow (Q) = 5.5000 m^3/s, pressure rise (\Delta p) = 34,000 Pa.

4. Step 4 — Substitute the given values:

   $$\eta = \dfrac{5.5000 34000}{138164}$$

5. Step 5 — Evaluate:

   $$\eta = 1.3535$$

6. Step 6 — Check: returning \eta = 1.3535 to

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

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

Why the other options are there

• 2.7069 — kept a factor of two that cancels in the correct rearrangement.
• 0.6767 — dropped that same factor in the other direction.
• 1.4888 — 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) = 8.4000 m^3/s; pressure rise (\Delta p) = 26,900 Pa; efficiency (\eta) = 0.6100, 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) = 8.4000 m^3/s, pressure rise (\Delta p) = 26,900 Pa, efficiency (\eta) = 0.6100.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{8.4000 26900}{0.6100}$$

5. Step 5 — Evaluate:

   $$W = 370426\ \text{W}$$

6. Step 6 — Check: returning W = 370,426 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

• 740,852 — kept a factor of two that cancels in the correct rearrangement.
• 185,213 — dropped that same factor in the other direction.
• 407,469 — 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) = 170,637 W; pressure rise (\Delta p) = 11,500 Pa; efficiency (\eta) = 0.5700, 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) = 170,637 W, pressure rise (\Delta p) = 11,500 Pa, efficiency (\eta) = 0.5700.

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{170637 0.5700}{11500}$$

5. Step 5 — Evaluate:

   Q = 8.4577\ \text{m^3/s}

6. Step 6 — Check: returning Q = 8.4577 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

• 16.9153 — kept a factor of two that cancels in the correct rearrangement.
• 4.2288 — dropped that same factor in the other direction.
• 9.3034 — 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) = 104,396 W; volumetric flow (Q) = 6.6000 m^3/s; pressure rise (\Delta p) = 50,600 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) = 104,396 W, volumetric flow (Q) = 6.6000 m^3/s, pressure rise (\Delta p) = 50,600 Pa.

4. Step 4 — Substitute the given values:

   $$\eta = \dfrac{6.6000 50600}{104396}$$

5. Step 5 — Evaluate:

   $$\eta = 3.1990$$

6. Step 6 — Check: returning \eta = 3.1990 to

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

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

Why the other options are there

• 6.3979 — kept a factor of two that cancels in the correct rearrangement.
• 1.5995 — dropped that same factor in the other direction.
• 3.5189 — 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) = 7.4000 m^3/s; pressure rise (\Delta p) = 19,800 Pa; efficiency (\eta) = 0.7700, 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) = 7.4000 m^3/s, pressure rise (\Delta p) = 19,800 Pa, efficiency (\eta) = 0.7700.

4. Step 4 — Substitute the given values:

   $$W = \dfrac{7.4000 19800}{0.7700}$$

5. Step 5 — Evaluate:

   $$W = 190286\ \text{W}$$

6. Step 6 — Check: returning W = 190,286 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

• 380,571 — kept a factor of two that cancels in the correct rearrangement.
• 95,143 — dropped that same factor in the other direction.
• 209,314 — rounded an intermediate value before the final step.

Reference: FE Handbook — Fans, Blowers, and Compressors