Question

Water is flowing in a 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 pressures at $A$ and $B$ are equal for any shape of the tube.
• B. The pressures are never equal.
• C. The pressures are equal if tube has a uniform cross-section.
• D. The pressures may be equal even if the tube has a nonuniform cross-section.

Answer 1

Answer: (C), (D)

The pressures are equal if tube has a uniform cross-section.
The pressures may be equal even if the tube has a nonuniform cross-section.

By using Bernoulli equation we can show that is A and B have same cross section ,then pressure at A= B

$P_A+\rho V_A^2/2=P_B+\rho V_b^2/2$

also $A_A{V}_A=A_B{V}_B$ and $A_A=A_B$

so $V_A=V_B\Rightarrow P_A=P_B$

if cross section is nonuniform and fluid is compressible then also pressure can be equal.