turbulent flow impeller mixer power requirement for rapid mix Given impeller constant (K_T) = 5.8500; fluid density (rho) = 995.0 kg/m^3; rotational speed (N) = 4.3000 rev/s; impeller diameter (D_i) = 0.5700 m, determine the power input (P) in W.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• 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.
• A turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for P:

   $$P = K_T\rho N^3 D_i^5$$

3. Step 3 — List the givens: impeller constant (K_T) = 5.8500, fluid density (rho) = 995.0 kg/m^3, rotational speed (N) = 4.3000 rev/s, impeller diameter (D_i) = 0.5700 m.

4. Step 4 — Substitute the given values:

   $$P = K_T995.0 4.3000^3 D_i^5$$

5. Step 5 — Evaluate:

   $$P = 27846\ \text{W}$$

6. Step 6 — Check: returning P = 27,846 W to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 55,691 — kept a factor of two that cancels in the correct rearrangement.
• 13,923 — dropped that same factor in the other direction.
• 30,630 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent flow impeller mixer design in a coagulation basin Given impeller constant (K_T) = 3.7500; fluid density (rho) = 999.5 kg/m^3; impeller diameter (D_i) = 1.0200 m; power input (P) = 33,767 W, determine the rotational speed (N) in rev/s.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• Everything except N is given, so isolate N 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 turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for N:

   $$N = \sqrt[3]{\dfrac{P}{K_T\rho D_i^5}}$$

3. Step 3 — List the givens: impeller constant (K_T) = 3.7500, fluid density (rho) = 999.5 kg/m^3, impeller diameter (D_i) = 1.0200 m, power input (P) = 33,767 W.

4. Step 4 — Substitute the given values:

   $$N = \sqrt[3]{\dfrac{33767}{K_T999.5 D_i^5}}$$

5. Step 5 — Evaluate:

   $$N = 2.0132\ \text{rev/s}$$

6. Step 6 — Check: returning N = 2.0132 rev/s to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 4.0265 — kept a factor of two that cancels in the correct rearrangement.
• 1.0066 — dropped that same factor in the other direction.
• 2.2145 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent impeller flow mixer power calculation for flocculation Given impeller constant (K_T) = 2.0000; fluid density (rho) = 992.0 kg/m^3; rotational speed (N) = 0.8500 rev/s; power input (P) = 23,718 W, determine the impeller diameter (D_i) in m.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• Everything except D_i is given, so isolate D_i 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 turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for D_i:

   $$D_{i} = \left(\dfrac{P}{K_T\rho N^3}\right)^{1/5}$$

3. Step 3 — List the givens: impeller constant (K_T) = 2.0000, fluid density (rho) = 992.0 kg/m^3, rotational speed (N) = 0.8500 rev/s, power input (P) = 23,718 W.

4. Step 4 — Substitute the given values:

   $$D_{i} = \left(\dfrac{23718}{K_T992.0 0.8500^3}\right)^{1/5}$$

5. Step 5 — Evaluate:

   $$D_{i} = 1.8107\ \text{m}$$

6. Step 6 — Check: returning D_i = 1.8107 m to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 3.6215 — kept a factor of two that cancels in the correct rearrangement.
• 0.9054 — dropped that same factor in the other direction.
• 1.9918 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent flow impeller mixer power requirement for rapid mix Given impeller constant (K_T) = 1.0500; fluid density (rho) = 995.5 kg/m^3; rotational speed (N) = 1.7500 rev/s; impeller diameter (D_i) = 1.2100 m, determine the power input (P) in W.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• 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.
• A turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for P:

   $$P = K_T\rho N^3 D_i^5$$

3. Step 3 — List the givens: impeller constant (K_T) = 1.0500, fluid density (rho) = 995.5 kg/m^3, rotational speed (N) = 1.7500 rev/s, impeller diameter (D_i) = 1.2100 m.

4. Step 4 — Substitute the given values:

   $$P = K_T995.5 1.7500^3 D_i^5$$

5. Step 5 — Evaluate:

   $$P = 14530\ \text{W}$$

6. Step 6 — Check: returning P = 14,530 W to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 29,060 — kept a factor of two that cancels in the correct rearrangement.
• 7,265 — dropped that same factor in the other direction.
• 15,983 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent flow impeller mixer design in a coagulation basin Given impeller constant (K_T) = 0.7000; fluid density (rho) = 995.0 kg/m^3; impeller diameter (D_i) = 0.6700 m; power input (P) = 46,243 W, determine the rotational speed (N) in rev/s.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• Everything except N is given, so isolate N 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 turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for N:

   $$N = \sqrt[3]{\dfrac{P}{K_T\rho D_i^5}}$$

3. Step 3 — List the givens: impeller constant (K_T) = 0.7000, fluid density (rho) = 995.0 kg/m^3, impeller diameter (D_i) = 0.6700 m, power input (P) = 46,243 W.

4. Step 4 — Substitute the given values:

   $$N = \sqrt[3]{\dfrac{46243}{K_T995.0 D_i^5}}$$

5. Step 5 — Evaluate:

   $$N = 7.8931\ \text{rev/s}$$

6. Step 6 — Check: returning N = 7.8931 rev/s to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 15.7863 — kept a factor of two that cancels in the correct rearrangement.
• 3.9466 — dropped that same factor in the other direction.
• 8.6825 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent impeller flow mixer power calculation for flocculation Given impeller constant (K_T) = 3.6500; fluid density (rho) = 999.5 kg/m^3; rotational speed (N) = 3.0000 rev/s; power input (P) = 32,887 W, determine the impeller diameter (D_i) in m.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• Everything except D_i is given, so isolate D_i 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 turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for D_i:

   $$D_{i} = \left(\dfrac{P}{K_T\rho N^3}\right)^{1/5}$$

3. Step 3 — List the givens: impeller constant (K_T) = 3.6500, fluid density (rho) = 999.5 kg/m^3, rotational speed (N) = 3.0000 rev/s, power input (P) = 32,887 W.

4. Step 4 — Substitute the given values:

   $$D_{i} = \left(\dfrac{32887}{K_T999.5 3.0000^3}\right)^{1/5}$$

5. Step 5 — Evaluate:

   $$D_{i} = 0.8030\ \text{m}$$

6. Step 6 — Check: returning D_i = 0.8030 m to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 1.6060 — kept a factor of two that cancels in the correct rearrangement.
• 0.4015 — dropped that same factor in the other direction.
• 0.8833 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent flow impeller mixer power requirement for rapid mix Given impeller constant (K_T) = 4.9000; fluid density (rho) = 1,000 kg/m^3; rotational speed (N) = 0.9500 rev/s; impeller diameter (D_i) = 0.9900 m, determine the power input (P) in W.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• 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.
• A turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for P:

   $$P = K_T\rho N^3 D_i^5$$

3. Step 3 — List the givens: impeller constant (K_T) = 4.9000, fluid density (rho) = 1,000 kg/m^3, rotational speed (N) = 0.9500 rev/s, impeller diameter (D_i) = 0.9900 m.

4. Step 4 — Substitute the given values:

   $$P = K_T1000 0.9500^3 D_i^5$$

5. Step 5 — Evaluate:

   $$P = 3995\ \text{W}$$

6. Step 6 — Check: returning P = 3,995 W to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 7,990 — kept a factor of two that cancels in the correct rearrangement.
• 1,998 — dropped that same factor in the other direction.
• 4,395 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent flow impeller mixer design in a coagulation basin Given impeller constant (K_T) = 0.7000; fluid density (rho) = 999.0 kg/m^3; impeller diameter (D_i) = 0.7600 m; power input (P) = 49,594 W, determine the rotational speed (N) in rev/s.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• Everything except N is given, so isolate N 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 turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for N:

   $$N = \sqrt[3]{\dfrac{P}{K_T\rho D_i^5}}$$

3. Step 3 — List the givens: impeller constant (K_T) = 0.7000, fluid density (rho) = 999.0 kg/m^3, impeller diameter (D_i) = 0.7600 m, power input (P) = 49,594 W.

4. Step 4 — Substitute the given values:

   $$N = \sqrt[3]{\dfrac{49594}{K_T999.0 D_i^5}}$$

5. Step 5 — Evaluate:

   $$N = 6.5398\ \text{rev/s}$$

6. Step 6 — Check: returning N = 6.5398 rev/s to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 13.0796 — kept a factor of two that cancels in the correct rearrangement.
• 3.2699 — dropped that same factor in the other direction.
• 7.1938 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent impeller flow mixer power calculation for flocculation Given impeller constant (K_T) = 3.5000; fluid density (rho) = 992.0 kg/m^3; rotational speed (N) = 0.5000 rev/s; power input (P) = 2,722 W, determine the impeller diameter (D_i) in m.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• Everything except D_i is given, so isolate D_i 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 turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for D_i:

   $$D_{i} = \left(\dfrac{P}{K_T\rho N^3}\right)^{1/5}$$

3. Step 3 — List the givens: impeller constant (K_T) = 3.5000, fluid density (rho) = 992.0 kg/m^3, rotational speed (N) = 0.5000 rev/s, power input (P) = 2,722 W.

4. Step 4 — Substitute the given values:

   $$D_{i} = \left(\dfrac{2722}{K_T992.0 0.5000^3}\right)^{1/5}$$

5. Step 5 — Evaluate:

   $$D_{i} = 1.4437\ \text{m}$$

6. Step 6 — Check: returning D_i = 1.4437 m to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 2.8874 — kept a factor of two that cancels in the correct rearrangement.
• 0.7219 — dropped that same factor in the other direction.
• 1.5881 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer

turbulent flow impeller mixer power requirement for rapid mix Given impeller constant (K_T) = 4.7500; fluid density (rho) = 993.0 kg/m^3; rotational speed (N) = 1.6500 rev/s; impeller diameter (D_i) = 0.2200 m, determine the power input (P) in W.

Start with the thinking

• The governing relation printed in this handbook section is Turbulent Flow Impeller Mixer.
• 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.
• A turbulent flow impeller mixer requires power proportional to impeller speed and diameter for rapid mixing in a basin.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$P = K_T \rho N^3 D_i^5$$

2. Step 2 — Rearrange symbolically for P:

   $$P = K_T\rho N^3 D_i^5$$

3. Step 3 — List the givens: impeller constant (K_T) = 4.7500, fluid density (rho) = 993.0 kg/m^3, rotational speed (N) = 1.6500 rev/s, impeller diameter (D_i) = 0.2200 m.

4. Step 4 — Substitute the given values:

   $$P = K_T993.0 1.6500^3 D_i^5$$

5. Step 5 — Evaluate:

   $$P = 10.9196\ \text{W}$$

6. Step 6 — Check: returning P = 10.9196 W to

   $$P = K_T \rho N^3 D_i^5$$

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

Why the other options are there

• 21.8393 — kept a factor of two that cancels in the correct rearrangement.
• 5.4598 — dropped that same factor in the other direction.
• 12.0116 — rounded an intermediate value before the final step.

Reference: FE Handbook — Turbulent Flow Impeller Mixer