Concept explainers
A horizontal pipe has an abrupt expansion from
Answers: 423 kPa, 17.3 kPa
The value of the downstream pressure.
The error which occurs when the Bernoulli's equation is used.
Answer to Problem 61P
The value of the downstream pressure
The error in downstream pressure due to Bernoulli's equation is
Explanation of Solution
Given information:
The velocity of water in the smaller section is
Write the expression for the cross sectional flow area for smaller section.
Here, the diameter of the small section is
Write the expression for the cross sectional flow area for bigger section.
Here, the diameter of the big pipe is
Write the expression for the velocity at bigger section using continuity equation.
Here, the velocity at the small section is
Write the expression for the loss coefficient for expansion based on the velocity in the smaller section.
Here, the correction factor for the kinetic energy is
Write the expression for the head loss due to sudden expansion from smaller section to bigger section.
Here, the gravitational acceleration is
Write the expression for the Bernoulli's equation.
Here, the smaller section pressure is
Write the expression for the real Bernoulli's equation.
Here, the downstream pressure using Bernoulli's equation is
Write the expression for the error in pressure due to use of Bernoulli's equation.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the downstream pressure
Substitute
Substitute
The error in downstream pressure due to Bernoulli's equation is
Conclusion:
The value of downstream pressure
The error in downstream pressure due to Bernoulli's equation is
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