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A handheld bicycle pump can be used as an atomizer to

Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala ISBN: 9780071284219 39

Solution for problem 55P Chapter 5

Fluid Mechanics | 2nd Edition

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Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala

Fluid Mechanics | 2nd Edition

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Problem 55P Problem 55P

A handheld bicycle pump can be used as an atomizer to generate a fine mist of paint or pesticide by forcing air at a high velocity through a small hole and placing a short tube between the liquid reservoir and the high-speed air jet. The pressure across a subsonic jet exposed to the atmosphere is nearly atmospheric, and the surface of the liquid in the reservoir is also open to atmospheric pressure. In light of this, explain how the liquid is sucked up the tube.Hint: Read Sec. 5-4 carefully.

Step-by-Step Solution:
Solution to 55P

Step 1</p>

We need to find how the liquid is sucked up the tube. To explain this we need to understand the problem using the Bernoulli's equation.

Consider the diagram:

Here we have taken four points. Point 1 is exactly at the nozzle of the pump. Point 2 is at a distance from the jet stream horizontally from the pump. Point 3 is somewhere at the midpoint of the jet stream. And point 4 is at the reservoir.

Considering the reservoir at a depth h below the pump, we will assume that z1, z2 and z3 is zero.

z4=-h

.As given in the question, P2, P4 is equal to Patm Is at atmospheric pressure. And the pressure at P1 and P3 are also same.

The velocity of points 2, 3 and 4 are considered as zero.

Step 2</p>

From Bernoulli's theorem

Where P=PRESSURE, V=VELOCITY, z=Height, ρ=density, g=acceleration due to gravity.

z3=0m, z4=-h

v3=v4=0m/s

P4=Patm , P3=P1

..................................(1)

z1=0m, z2=0m

v2=0m/s

....................................................(2)

Combining the equation (1) and (2)

Step 3 of 3

Chapter 5, Problem 55P is Solved
Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

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