Water flows through 150 mm diameter pipe AB 400 m longThe point B is 20 m above A. The discharge through the pipe is 0.02 m³/sec from A to BFind the pressure at A if the pressure at B is 200 kPa. Take f= 0.006.
Water flows through 150 mm diameter pipe AB 400 m longThe point B is 20 m above A. The discharge through the pipe is 0.02 m³/sec from A to BFind the pressure at A if the pressure at B is 200 kPa. Take f= 0.006.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Fluid Mechanics Problem
#### Problem Statement:
Water flows through a 150 mm diameter pipe AB which is 400 m long. The point B is 20 m above point A. The discharge through the pipe is 0.02 m³/sec from point A to point B. Find the pressure at point A if the pressure at point B is 200 kPa. Assume the Darcy-Weisbach friction factor \( f = 0.006 \).
#### Given Data:
- Pipe diameter, \( D = 150 \) mm = 0.15 m
- Pipe length, \( L = 400 \) m
- Height difference, \( z = 20 \) m
- Discharge, \( Q = 0.02 \) m³/sec
- Pressure at B, \( P_B = 200 \) kPa = 200,000 Pa
- Friction factor, \( f = 0.006 \)
#### Objective:
Calculate the pressure at point A, \( P_A \).
#### Applicable Formulas:
1. **Continuity Equation** for flow through a pipe:
\[ Q = A \cdot V \]
where \( A \) is the cross-sectional area of the pipe and \( V \) is the velocity of the fluid.
2. **Cross-sectional Area of Pipe**:
\[ A = \frac{\pi D^2}{4} \]
3. **Bernoulli’s Equation** including head loss due to friction:
\[ P_A + \frac{1}{2} \rho V_A^2 + \rho g z_A + h_f = P_B + \frac{1}{2} \rho V_B^2 + \rho g z_B \]
where:
- \( h_f \) is the head loss due to friction, which can be found using Darcy-Weisbach equation.
4. **Head Loss due to Friction** (Darcy-Weisbach equation):
\[ h_f = f \cdot \frac{L}{D} \cdot \frac{V^2}{2g} \]
where \( g \) is the acceleration due to gravity and \( \rho \) is the density of water.
### Steps to Solution:
1. Calculate the cross-sectional area \( A \) of the pipe.
2. Determine the velocity \( V \) of water using the continuity equation.
3. Apply Bernoulli’s equation accounting for head](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b2f6d1e-6332-46ff-aac3-69fac171d186%2Fdc8e9446-04a6-404f-beaa-7960e70c8d3e%2F0yrb45_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Fluid Mechanics Problem
#### Problem Statement:
Water flows through a 150 mm diameter pipe AB which is 400 m long. The point B is 20 m above point A. The discharge through the pipe is 0.02 m³/sec from point A to point B. Find the pressure at point A if the pressure at point B is 200 kPa. Assume the Darcy-Weisbach friction factor \( f = 0.006 \).
#### Given Data:
- Pipe diameter, \( D = 150 \) mm = 0.15 m
- Pipe length, \( L = 400 \) m
- Height difference, \( z = 20 \) m
- Discharge, \( Q = 0.02 \) m³/sec
- Pressure at B, \( P_B = 200 \) kPa = 200,000 Pa
- Friction factor, \( f = 0.006 \)
#### Objective:
Calculate the pressure at point A, \( P_A \).
#### Applicable Formulas:
1. **Continuity Equation** for flow through a pipe:
\[ Q = A \cdot V \]
where \( A \) is the cross-sectional area of the pipe and \( V \) is the velocity of the fluid.
2. **Cross-sectional Area of Pipe**:
\[ A = \frac{\pi D^2}{4} \]
3. **Bernoulli’s Equation** including head loss due to friction:
\[ P_A + \frac{1}{2} \rho V_A^2 + \rho g z_A + h_f = P_B + \frac{1}{2} \rho V_B^2 + \rho g z_B \]
where:
- \( h_f \) is the head loss due to friction, which can be found using Darcy-Weisbach equation.
4. **Head Loss due to Friction** (Darcy-Weisbach equation):
\[ h_f = f \cdot \frac{L}{D} \cdot \frac{V^2}{2g} \]
where \( g \) is the acceleration due to gravity and \( \rho \) is the density of water.
### Steps to Solution:
1. Calculate the cross-sectional area \( A \) of the pipe.
2. Determine the velocity \( V \) of water using the continuity equation.
3. Apply Bernoulli’s equation accounting for head
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