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Question

In the following figure, flow of a liquid through a horizontal pipe has been shown. Three tubes A,B and C are connected to the pipe. The radii of the tubes A,B and C at the junction are respectively 2 cm,1 cm and 2 cm. It can be said that the


A
height of the liquid in the tube B is maximum
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B
height of the liquid in the tubes A and B is the same
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C
height of the liquid in all the three tubes is the same
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D
height of the liquid in the tubes A and C is the same.
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Solution

The correct option is D height of the liquid in the tubes A and C is the same.
Cross-sectional areas of both the tubes A and C are the same and pipe is horizontal.
Hence, according to equation of continuity,
Av=constantvA=vC
According to Bernoulli's theorem,
P+12ρv2+ρgh=constant ...(i)
Pipe is horizontal (No change in elevation of fluid) i.e h= constant.
PA=PC
So, we can conclude that pressure remains same at A and C.
For liquid column in the vertical tube, the relation between height of liquid and pressure at the point is,
P=ρgh
PA=PChA=hC
Hence, height of liquid will be the same in both the tubes A and C.

Similarly, vB>vA, as the cross-sectional area at B is lower.
According to Bernoulli's theorem,
P+12ρv2+ρgh=constant
Since KEB>KEA, in accordance with Bernoulli's equation, we get:
PB<PA [since h is constant here also]
From P=ρgh, hA>hB

correct option is (d)

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