A venturi meter with a 275.0 mm approach pipe and a throat diameter ratio β = 0.55 registers a differential pressure of 33 kPa on water. With a meter coefficient of 0.98, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.55(275.0) = 151.3 mm, A_{2} = 0.01797 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.55^{4} = 0.9085$$

4. Velocity term

   $$\sqrt[2(33\times1000)/1000] = 8.12$$

5. Substituting

   $$Q = 0.98(0.01797)(8.12)/\sqrt0.9085 = 0.1501 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 8.35 m/s$$

Why the other options are there

• 0.1430 m³/s (β⁴ correction omitted)
• 0.1531 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 250.0 mm approach pipe and a throat diameter ratio β = 0.60 registers a differential pressure of 16 kPa on water. With a meter coefficient of 0.98, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.60(250.0) = 150.0 mm, A_{2} = 0.01767 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.60^{4} = 0.8704$$

4. Velocity term

   $$\sqrt[2(16\times1000)/1000] = 5.66$$

5. Substituting

   $$Q = 0.98(0.01767)(5.66)/\sqrt0.8704 = 0.1050 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 5.94 m/s$$

Why the other options are there

• 0.0980 m³/s (β⁴ correction omitted)
• 0.1071 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 175.0 mm approach pipe and a throat diameter ratio β = 0.60 registers a differential pressure of 76 kPa on water. With a meter coefficient of 0.96, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.60(175.0) = 105.0 mm, A_{2} = 0.00866 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.60^{4} = 0.8704$$

4. Velocity term

   $$\sqrt[2(76\times1000)/1000] = 12.33$$

5. Substituting

   $$Q = 0.96(0.00866)(12.33)/\sqrt0.8704 = 0.1099 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 12.69 m/s$$

Why the other options are there

• 0.1025 m³/s (β⁴ correction omitted)
• 0.1144 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 300.0 mm approach pipe and a throat diameter ratio β = 0.45 registers a differential pressure of 45 kPa on water. With a meter coefficient of 0.97, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.45(300.0) = 135.0 mm, A_{2} = 0.01431 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.45^{4} = 0.9590$$

4. Velocity term

   $$\sqrt[2(45\times1000)/1000] = 9.49$$

5. Substituting

   $$Q = 0.97(0.01431)(9.49)/\sqrt0.9590 = 0.1345 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 9.40 m/s$$

Why the other options are there

• 0.1317 m³/s (β⁴ correction omitted)
• 0.1387 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 275.0 mm approach pipe and a throat diameter ratio β = 0.45 registers a differential pressure of 30 kPa on water. With a meter coefficient of 0.98, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.45(275.0) = 123.8 mm, A_{2} = 0.01203 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.45^{4} = 0.9590$$

4. Velocity term

   $$\sqrt[2(30\times1000)/1000] = 7.75$$

5. Substituting

   $$Q = 0.98(0.01203)(7.75)/\sqrt0.9590 = 0.0932 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 7.75 m/s$$

Why the other options are there

• 0.0913 m³/s (β⁴ correction omitted)
• 0.0951 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 150.0 mm approach pipe and a throat diameter ratio β = 0.45 registers a differential pressure of 41 kPa on water. With a meter coefficient of 0.98, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.45(150.0) = 67.5 mm, A_{2} = 0.00358 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.45^{4} = 0.9590$$

4. Velocity term

   $$\sqrt[2(41\times1000)/1000] = 9.06$$

5. Substituting

   $$Q = 0.98(0.00358)(9.06)/\sqrt0.9590 = 0.0324 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 9.06 m/s$$

Why the other options are there

• 0.0318 m³/s (β⁴ correction omitted)
• 0.0331 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 300.0 mm approach pipe and a throat diameter ratio β = 0.45 registers a differential pressure of 84 kPa on water. With a meter coefficient of 0.99, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.45(300.0) = 135.0 mm, A_{2} = 0.01431 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.45^{4} = 0.9590$$

4. Velocity term

   $$\sqrt[2(84\times1000)/1000] = 12.96$$

5. Substituting

   $$Q = 0.99(0.01431)(12.96)/\sqrt0.9590 = 0.1876 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 13.10 m/s$$

Why the other options are there

• 0.1837 m³/s (β⁴ correction omitted)
• 0.1895 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 225.0 mm approach pipe and a throat diameter ratio β = 0.50 registers a differential pressure of 81 kPa on water. With a meter coefficient of 0.97, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.50(225.0) = 112.5 mm, A_{2} = 0.00994 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.50^{4} = 0.9375$$

4. Velocity term

   $$\sqrt[2(81\times1000)/1000] = 12.73$$

5. Substituting

   $$Q = 0.97(0.00994)(12.73)/\sqrt0.9375 = 0.1267 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 12.75 m/s$$

Why the other options are there

• 0.1227 m³/s (β⁴ correction omitted)
• 0.1307 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 275.0 mm approach pipe and a throat diameter ratio β = 0.60 registers a differential pressure of 89 kPa on water. With a meter coefficient of 0.97, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.60(275.0) = 165.0 mm, A_{2} = 0.02138 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.60^{4} = 0.8704$$

4. Velocity term

   $$\sqrt[2(89\times1000)/1000] = 13.34$$

5. Substituting

   $$Q = 0.97(0.02138)(13.34)/\sqrt0.8704 = 0.2966 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 13.87 m/s$$

Why the other options are there

• 0.2767 m³/s (β⁴ correction omitted)
• 0.3058 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement

A venturi meter with a 275.0 mm approach pipe and a throat diameter ratio β = 0.40 registers a differential pressure of 54 kPa on water. With a meter coefficient of 0.98, compute the throat diameter, throat velocity and the discharge.

Start with the thinking

• The (1 − β⁴) term corrects for the approach velocity — dropping it overestimates flow.
• A venturi recovers most of the pressure drop, unlike an orifice plate.

Step-by-step solution

1. Throat

   $$D_{2} = 0.40(275.0) = 110.0 mm, A_{2} = 0.00950 m^{2}$$

2. Formula

   $$Q = \dfrac{C_v A_2}{\sqrt{1-\beta^4}}\sqrt{\dfrac{2\Delta p}{\rho}}$$

3. β⁴ term

   $$1 - 0.40^{4} = 0.9744$$

4. Velocity term

   $$\sqrt[2(54\times1000)/1000] = 10.39$$

5. Substituting

   $$Q = 0.98(0.00950)(10.39)/\sqrt0.9744 = 0.0980 m^{3}/s$$

6. Throat velocity

   $$V_{2} = Q/A_{2} = 10.32 m/s$$

Why the other options are there

• 0.0968 m³/s (β⁴ correction omitted)
• 0.1001 m³/s (coefficient omitted)

Reference: FE Reference Handbook — Fluid Mechanics → Fluid Flow Measurement