Mechanical Properties of Fluids

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Question : 16
Total: 31
The cylindrical tube of a spray pump has a cross-section of 8.0cm2 on one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5m min1, what is the speed of ejection of the liquid through the holes?
Solution:  
Here, cross-section of the tube, a1=8.0 cm2=8.0×104 m2
The speed of liquid in the tube, v1=1.5m min1=
1.5
60
m
s1

=0.025 m s1
diameter of a hole, D=1.0 mm=103 m
Therefore, cross-section of a hole,
πD2
4
=
π
4
×(103 )2

=
π
4
×106 m2

Therefore, total cross-section of 40 holes, a2=
π
4
×106
×40 m2

If v2 is the speed of ejection of the liquid through the holes, then a1v1=a2v2
or v2=
a1v1
a2

=
8.0×104×0.025
(
π
4
)
×106
×40

=0.637 ms1.
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