Water from a reservoir is raised in a vertical tube of internal diameter D =30 cm under the influence of the pulling force F of a piston. Determine the force needed to raise the water to a height of h = 1.5 m above the free surface. What would your response be for h = 3 m? Also, taking the atmospheric pressure to be 96 kPa, plot the absolute water pressure at the piston face as h varies from 0 to 3 m.
FIGURE P3-26
The force needed to raise the water to a height of
The force needed to raise the water to a height of
The force needed to raise the water to a height of
Answer to Problem 26P
The force needed to raise the water to a height of
The force needed to raise the water to a height of
The force needed to raise the water to a height of
Explanation of Solution
Given information:
The internal diameter of the piston is
Write the expression for the pressure exerted by a fluid
Here, the pressure exerted by a fluid is
Write the expression for area.
Here, cross-section area of the piston is
Here, weight exerted by the fluid column is
Substitute the
Write the expression for net vertical force.
Here, force required to raise the water is
Write the expression for absolute pressure acting on the piston face.
Here, absolute pressure is
Calculation:
Substitute
Substitute
Substitute
Here, the force required to raise the water is at height of
Substitute
Substitute
Substitute
Here, the force required to raise the water is at height of
Substitute
Substitute
Substitute
Here, the force required to raise the water is at height of
Substitute
Here, absolute pressure at height
Substitute
Here, absolute pressure at height
Substitute
Here, absolute pressure at height
The following Table-(1) shows the water pressure at different height of water level in the tube.
Water level | Absolute Pressure |
The following figure variation of absolute water verse height of water in the tube.
Figure-(1)
Conclusion:
The force needed to raise the water to a height of
The force needed to raise the water to a height of
The force needed to raise the water to a height of
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Chapter 3 Solutions
Fluid Mechanics: Fundamentals and Applications
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