GATE CE 2017 Set 1 — Question 49

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NAT+2 / -0HardMomentum EquationFluid Kinematics & DynamicsWater Resources EngineeringBernoulli's Equation

Water Resources Engineering → Fluid Kinematics & Dynamics → Bernoulli's Equation

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Question

Water flows through a 9090^\circ bend in a horizontal plane as depicted in the figure.
A $90^\circ$ pipe bend in a horizontal plane with sections 1-1 and 2-2 marked. Forces $F_x$ and $F_y$ are shown. Pressures $P_1$ and $P_2$ are indicated. Section 2-2 is open to atmosphere.
A pressure of 140 kPa140\text{ kPa} is measured at Section 1-1. The inlet diameter marked at Section 1-1 is 27π cm\frac{27}{\sqrt{\pi}}\text{ cm}, while the nozzle diameter marked at Section 2-2 is 14π cm\frac{14}{\sqrt{\pi}}\text{ cm}. Assume the following:
(i) Acceleration due to gravity =10 m/s2= 10\text{ m/s}^2.
(ii) Weights of both the bent pipe segment as well as water are negligible.
(iii) Friction across the bend is negligible.
The magnitude of the force (in kN, up to two decimal places) that would be required to hold the pipe section is ____________
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