ESC2C5 Problem Set 6 Answers

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ES2B0 - Fluid Mechanics
Model Answers to Example Questions (Set 6)

Question 1: Bernoulli and Continuity

In Figure 1 the open jet of water at 20 exits a nozzle into sea‐level air and strikes a
stagnation tube as shown.




Figure 1

If the pressure at the centreline at section 1 is 110 kPa, and losses are neglected, estimate
(a) the mass flow in kg⁄s and (b) the height H of the fluid in the stagna on tube.



SOLUTION

Continuity between pipe and jet:




4 4




Bernoulli between pipe and jet:

1 1
2 2
Here, and (atmospheric pressure) then,

1
2
Combine Bernoulli and Continuity,

, 2



1
2

998 4
110000 101350 1
2 12

4.19 /

Then the mass flow is,

998 0.04 4.19
4
. /



The water in the stagnation tube will rise above the jet surface by an amount equal to
the stagnation pressure head of the jet:

4.19
0.02 0.02 0.89
2 2 9.81

.



Question 2: Dimensional analysis

During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional
analysis to estimate the wave speed of an atomic bomb explosion. He assumed that the
blast wave radius was a function of energy released , air density , and time . Use
dimensional reasoning to show how wave radius must vary with time.




SOLUTION

The proposed function is , , . There are four variables 4 and three primary
dimensions , 3 , thus we expect 4 3 1 pi group. List the
dimensions:

; / ; / ;

Assume arbitrary exponents and make the group dimensionless:

/ /