Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
8th Edition
ISBN: 9781119080701
Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein
Publisher: WILEY
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Question
Chapter 3.2, Problem 1P
To determine

Determine the fluid flow velocity in the duct.

Expert Solution & Answer
Check Mark

Answer to Problem 1P

The fluid flow velocity in the duct is u1=2(p2p1)ρ.

Explanation of Solution

The Bernoulli’s Equation can be used in many places not only in the pipe flow; the following are circumstances where the Bernoulli’s Equation shall be used in tanks as well as in open channels.

Circumference influenced by Bernoulli’s Equation.

  • Pitot tube.
  • Pitot static tube.
  • Venturimeter and orificemeter.
  • Flow over notches and weirs.

Pitot tube:

Pitot tube can be used to determine the velocity of fluid flow by connect with U-tube water gauge or with differential pressure gauge.

Sketch the part of Pitot tube of streamlines flow through the blunt body at uniform velocity as in Figure (1).

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version, Chapter 3.2, Problem 1P

Apply the Bernoulli’s Equation at duct fluid flow velocity of u1 and the pressure p1 to the velocity u2 at stagnation point 2 and the pressure p2.

  p1ρg+u122g+z1=p2ρg+u222g+z2        (I)

Here, the density fluid is ρ, the acceleration due to gravity is g and datum head with respect to center of tube at point 1 and point 2 is z.

Conclusion:

From the Figure (1), the datum head at point 1 and 2 will be same (z1=z2=z) and the velocity at stagnation point 2 equals to zero.

Substitute z for z1, z for z2 and 0 for u2 in Equation (I).

  p1ρg+u122g+z=p2ρg+02g+zp1ρg+u122g=p2ρgu122=p2ρp1ρu1=2(p2p1)ρ

Hence, the fluid flow velocity in the duct is u1=2(p2p1)ρ.

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Chapter 3 Solutions

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

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