Water is flowing streamline motion through a tube with its axis horizontal. Consider two points A and B in the tube at the same horizontal level.
a) The pressure at A and B are equal for any shape of the tube.
b) The pressure never equal
C) The pressure are equal if the tube has uniform cross-section
d) The pressure may be equal even if the tube has a nonuniform cross-section.

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c and d are correct

b and c are correct

All are correct

a, c and d are correct

answer is B.

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Detailed Solution

We can show using the Bernoulli equation that if A and B have the same cross section, then pressure at A = B.

$P_{A} + ρ \frac{{V_{A}}^{2}}{2} = P_{B} + ρ \frac{{V_{B}}^{2}}{2}$

$A_{A} V_{A} = A_{B} V_{B},$

$A_{A} = A_{B}$

$V_{A} = V_{B} \Rightarrow P_{A} = P_{B}$

Pressure can be equal if the cross section is nonuniform and the fluid is compressible.

Hence the correct answer is c and d are correct.

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