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Bernoulli's Equation and Control Volume Applications, Assignments of Fluid Mechanics

Indian Institute of Space Science and TechnologyFluid Mechanics

Topics included- application of bernaulli's theorem, determining force exerted by fluid on fixed bodies. Calculating torque about hinge points.

Typology: Assignments

2022/2023

Available from 03/05/2023

Shivayadav04
Shivayadav04 🇮🇳

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INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY
THIRUVANANTHAPURAM
B.Tech. Aerospace Engineering
AE213 FLUID MECHANICS
Assignment 3
Submission deadline: 30 September 2022
1. As shown in figure below, a liquid column of height his confined in a vertical tube of cross-sectional
area Aby a stopper. At t=0the stopper is suddenly removed, exposing the bottom of the liquid to
atmospheric pressure. Using a control volume analysis of mass and vertical momentum, derive the
differential equation for the downward motion V(t)of the liquid. Assume one-dimensional, incom-
pressible, frictionless flow.
2. Water flows through a circular nozzle, exits into the air as a jet, and strikes a plate, as shown in
figure below. The force required to hold the plate steady is 70 N. Assuming steady, frictionless, one-
dimensional flow, estimate (a) the velocities at inlet and exit sections of the nozzle and the mercury
manometer reading h.
3. A free liquid jet, as in figure below, has constant ambient pressure and negligible losses. For the fire
nozzle in the figure, what are (a) the minimum and (b) the maximum values of θfor which the water
jet will clear the corner of the building? For which case will the jet velocity be higher when it strikes
the roof of the building?
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INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY

THIRUVANANTHAPURAM

B.Tech. Aerospace Engineering

AE213 FLUID MECHANICS Assignment 3

Submission deadline: 30 September 2022

  1. As shown in figure below, a liquid column of height h is confined in a vertical tube of cross-sectional area A by a stopper. At t = 0 the stopper is suddenly removed, exposing the bottom of the liquid to atmospheric pressure. Using a control volume analysis of mass and vertical momentum, derive the differential equation for the downward motion V (t) of the liquid. Assume one-dimensional, incom- pressible, frictionless flow.
  2. Water flows through a circular nozzle, exits into the air as a jet, and strikes a plate, as shown in figure below. The force required to hold the plate steady is 70 N. Assuming steady, frictionless, one- dimensional flow, estimate (a) the velocities at inlet and exit sections of the nozzle and the mercury manometer reading h.
  3. A free liquid jet, as in figure below, has constant ambient pressure and negligible losses. For the fire nozzle in the figure, what are (a) the minimum and (b) the maximum values of θ for which the water jet will clear the corner of the building? For which case will the jet velocity be higher when it strikes the roof of the building?
  1. A necked-down section in a pipe flow (venturi), develops a low throat pressure that can aspirate fluid upward from a reservoir, as in figure below. Using Bernoulli’s equation with no losses, derive an expression for the velocity V 1 that is just sufficient to bring reservoir fluid into the throat.
  2. If losses are neglected in figure below, for what water level h will the flow begin to form vapor cavities at the throat of the nozzle?
  3. In the spillway flow in figure below, the flow is assumed uniform and hydrostatic at sections 1 and 2. If losses are neglected, compute (a) V 2 and (b) the force per unit width of the water on the spillway.