GATE ME 2026 Set 1 — Question 53
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
Water with a density of comes out of an industrial condenser through a horizontal pipe of radius at the flow rate of . The outlet of the pipe is connected to a coaxial diffuser of length using a flange to raise the pressure of water to atmospheric condition without any backflow. The inner radius (, in m) of the diffuser cross-section is expressed aswhere, represents the axial distance of the diffuser in m, from its inlet. Considering frictionless flow, the magnitude of the force exerted by the diffuser on the flange is ________ N (rounded off to 2 decimal places).
Correct answer
15.5 to 17.1
Solution
1.Convert flow rate to SI units:
.2.Determine inlet and outlet radii:
At inlet (): .At outlet (): .
3.Calculate cross-sectional areas:
..
4.Calculate velocities:
..
5.Apply Bernoulli's equation (frictionless flow):
.Assuming (gauge pressure),
.
6.Apply the momentum equation to the control volume:
where .
.
7.Magnitude of force:
The magnitude of the force exerted by the diffuser on the flange is .Continue learning with Success Tracker
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