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Two pipes move the same amount of ideal fluid in the same amount of time. One pipe has a 2 in. diameter; the other has a 3 in. diameter. In which pipe is the fluid pressure higher, assuming that all other conditions are the same?

a)3-in. pipe

b)2-in. pipe

c)same pressure in both

d)cannot be determined for an ideal fluid

Verified Answer :

By Bernoulli Theorem, We know, that for any two points in the pipe, total energy would be same. 

Pressure Energy + K.E. of 1st pipe = Pressure Energy + K.E. of 2nd pipe
[ No need to consider Potential energy as height isn't mentioned] 
P₁ + mv₁²/2 = P₂ + mv₂²/2

So, we know, P + mv²/2 = constant

As value of kinetic energy is larger in larger in 2 in. pipe [ 'cause area is indirectly proportional to velocity ], Value of pressure energy would be smaller in it. So, pressure energy will be higher in the pipe of 3 in.

In short, option A would be your correct answer.

Hope this helps!



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