Concept explainers
A pipe of varying inner diameter carries water. At point-1 the diameter is 20 cm and the pressure is 130 kPa. At point-2, which is 4.0 m higher than point-1, the diameter is 30 cm. If the flow is
The pressure atpoint
Answer to Problem 39SP
Solution:
Explanation of Solution
Given data:
At point
At point
The flowrate of the water is
At point
Point
Formula used:
Write the expression for discharge rate:
Here,
Write the expression for the equation of continuity:
Here,
Write the expression for Bernoulli’s equation:
If the density of the liquids is theconstant, then
At point
Write the expression for cross-section area of the pipe:
Here,
Explanation:
Draw the schematic diagram of the pipe having varying cross-section, and also, denote point
Recall the expression for cross-sectional area of the pipe at the point 1:
Here,
Substitute
Recall the expression for cross-sectional area of the pipe at the point 2:
Here,
Substitute
Recall the expression for the equation of continuity:
Consider
Substitute
Rewrite the expression for the equation of continuity:
Consider
Recall the expression for Bernoulli’s equation when the density of the water is constant:
Consider point 1 as a datum surface of reference point. Therefore,
Consider the density of water as
In is understood that
Solve the equation for
Conclusion:
Therefore, the pressure at the second side is
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Chapter 14 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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