Question

Water is flowing through a long horizontal tube. Let P_A and P_B be the pressures at two points A and B of the tube.

• A. P_A must be equal to P_B.
• B. P_A must be greater than P_B.
• C. P_A must be smaller than P_B.
• D. P_A = P_B only if the cross-sectional area at A and B are equal.

Answer 1

The correct option is D

P_A = P_B only if the cross-sectional area at A and B are equal.

Now if $A_1=A_{2}and{h}_1=h_2$
$\Rightarrow V_1=V_2{A}_1{V}_1=A_2{V}_2$
Also,$P_A+\stackrel{,}{\rho }g{h}_A+\frac{1}{2}\stackrel{,}{\rho }$ $V_A^2=P_B+\stackrel{,}{\rho }g{h}_B+\frac{1}{2}\stackrel{,}{\rho }{V}_B^2\Rightarrow P_A=P_B$
So if the cross-sectional area at A and B are equal
$P_A=P_B$ Hence (d)