Water is flowing into and discharging from a pipe U-section as shown in Fig. P6-77. At flange (1). the total absolute pressure is 200 kPa. and 55 kgs flows into the pipe. At flange (2), the total pressure is 150 kPa. At location (3). 15 kg/s of water discharges to the atmosphere, which is at 100 kPa. Detenume the total x- and z-forces at the two flanges connecting the pipe. Discuss the significance of gravity force for this problem. Take the inomentiun-flux correction
factor to be 1.03 throughout the pipes.
The forces along x-direction.
The net force along z-direction.
Answer to Problem 77P
The forces along x-direction is
The net force along z-direction is
Explanation of Solution
Given information:
The total absolute pressure at flange
Figure-(1) represents the free body diagram of U tube.
Figure-(1)
Expression for area of pipe,
Here, diameter of pipe is
Expression for velocity of flow,
Here, mass flow rate is
Expression for mass flow rate through pipe
Here, discharge through pipe
Expression for momentum equation in horizontal direction for pipe
Here, reaction force in horizontal direction for pipe
Expression for momentum equation along vertical direction in pipe
Expression for momentum equation in horizontal direction for pipe
Here, reaction force in horizontal direction for pipe
Expression for momentum equation along vertical direction in pipe
Expression for momentum equation along horizontal direction in pipe
Expression for momentum equation along vertical direction for pipe
Here, reaction force in vertical direction for pipe
Expression for net horizontal force,
Expression for net vertical reaction force,
Expression for weight per unit length for pipe
Here, density of water is
Expression for weight per unit length for pipe
Expression for weight for pipe
Expression for net vertical force,
Calculation:
Substitute
Substitute
Substitute
Refer to Table-A-3 "Properties of saturated water" to obtain density of water as
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The forces along x-direction is
The net force along z-direction is
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Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
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