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Question

The mass of liquid flowing per second per unit area of cross section of the tube is proportional to Px and vy, where P is the pressure difference and v is the velocity, then the relation between x and y is

A
x=y
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B
x=y
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C
y2=x
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D
y=x2
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Solution

The correct options are
B x=y
C y2=x
D y=x2
We have,
mAtPxvy
mAt=CPxvy

Using dimensional analysis:
[ML2T1]=[ML1T2]x[LT1]y
[ML2T1]=[MxLxT2x][LyTy]
[ML2T1]=[MxLyxT2xy]

Now just equating the powers of the respective dimensions, we have:
x=1
yx=2
2xy=1
y=1
x=y, y2=x and y=x2
.

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