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

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
icon
Related questions
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.
Transcribed Image Text:### 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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 7 images

Blurred answer
Knowledge Booster
Applied Fluid Mechanics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY