### Example 3:A pipe with a diameter of 50 cm carries water (at 10 °C) at a flow rate of 0.5 m³/s. A pump in the pipe is used to move the water from an elevation of 30 m to 40 m.The pressure at section 1 is 70 kPa gage, and the pressure at section 2 is 350 kPa gage. What power in kilowatts and in horsepower must be supplied to the flow by the pump?Assume:- \( h_L \) = 3 m of water- \( \alpha_1 = \alpha_2 = 1 \)#### Diagram Explanation:The diagram illustrates how water is being pumped through a system:- **System Overview**: The diagram shows a section of piping with a pump.- **Section 1**: - Elevation \( z_1 \) = 30 m - Pressure \( p_1 \) = 70 kPa gage - Velocity coefficient \( \alpha_1 = 1.0 \)- **Section 2**: - Elevation \( z_2 \) = 40 m - Pressure \( p_2 \) = 350 kPa gage - Velocity coefficient \( \alpha_2 = 1.0 \)- **Pipe Details**: - Pipe diameter \( D = 0.5 \) m - Head loss in the pipe is 3 m of water - Water flow rate \( Q = 0.5 \) m³/s#### Properties:Water at 10°C, with a specific weight \( \gamma = 9810 \) N/m³.This problem requires calculating the power supplied by the pump, taking into account the elevation change, pressure difference, head loss, and specific flow properties.

The diameter of the pipe, (D)=0.5 mThe volume flow rate of the water, (Q)=0.5 m3/sThe elevation at the inlet, (z1)=30mThe elevation at the exit, (z2)=40mThe pressure at the inlet, (P1)=70 kPaThe pressure at the exit, (P2)=350 kPaFor water Determine the power input to the pump.From Bernoulli's equation between point (1) and (2).Since, the diameter of the pipe is constant therefore Putting the given values.The power input to the pump.

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Example 3: A pipe 50 cm in diameter carries water (10 °C) at a rate of 0.5 m³/s. A pump in the pipe is used to move the water from an elevation of 30 m to 40 m. The pressure at section 1 is 70 kPa gage, and the pressure at section 2 is 350 kPa gage. What power in kilowatts and in horsepower must be supplied to the flow by the pump? Assume h₁ = 3 m of water and a₁ = α₂ = 1. Water is being pumped through a system. Z₁ = 30 m P₁ = 70 kPa gage a₁ 1.0 1 Pump 2₂ = 40 m P2= 350 kPa gag %₂= 1.0 Pipe D = 0.5 m Head loss in pipe = 3 m Water Q=0.5 m³/s Properties: Water (10°C, 1 atm, Table A.5): y = 9810 N/m³

Example 3: A pipe 50 cm in diameter carries water (10 °C) at a rate of 0.5 m³/s. A pump in the pipe is used to move the water from an elevation of 30 m to 40 m. The pressure at section 1 is 70 kPa gage, and the pressure at section 2 is 350 kPa gage. What power in kilowatts and in horsepower must be supplied to the flow by the pump? Assume h₁ = 3 m of water and a₁ = α₂ = 1. Water is being pumped through a system. Z₁ = 30 m P₁ = 70 kPa gage a₁ 1.0 1 Pump 2₂ = 40 m P2= 350 kPa gag %₂= 1.0 Pipe D = 0.5 m Head loss in pipe = 3 m Water Q=0.5 m³/s Properties: Water (10°C, 1 atm, Table A.5): y = 9810 N/m³

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Applied Fluid Mechanics

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

Question

### Example 3:

A pipe with a diameter of 50 cm carries water (at 10 °C) at a flow rate of 0.5 m³/s. A pump in the pipe is used to move the water from an elevation of 30 m to 40 m.

The pressure at section 1 is 70 kPa gage, and the pressure at section 2 is 350 kPa gage. What power in kilowatts and in horsepower must be supplied to the flow by the pump?

Assume:
- \( h_L \) = 3 m of water
- \( \alpha_1 = \alpha_2 = 1 \)

#### Diagram Explanation:

The diagram illustrates how water is being pumped through a system:

- **System Overview**: The diagram shows a section of piping with a pump.
- **Section 1**:
- Elevation \( z_1 \) = 30 m
- Pressure \( p_1 \) = 70 kPa gage
- Velocity coefficient \( \alpha_1 = 1.0 \)

- **Section 2**:
- Elevation \( z_2 \) = 40 m
- Pressure \( p_2 \) = 350 kPa gage
- Velocity coefficient \( \alpha_2 = 1.0 \)

- **Pipe Details**:
- Pipe diameter \( D = 0.5 \) m
- Head loss in the pipe is 3 m of water
- Water flow rate \( Q = 0.5 \) m³/s

#### Properties:

Water at 10°C, with a specific weight \( \gamma = 9810 \) N/m³.

This problem requires calculating the power supplied by the pump, taking into account the elevation change, pressure difference, head loss, and specific flow properties.

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