Question

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is $\upsilon$, what is the pressure at another point where the velocity of flow is $2\upsilon ;\rho$ being the density of water?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

According to Bernoulli's theorem, for a horizontal flow at a height h from ground level,

$P_1+\frac{1}{2}\rho {\upsilon }_1^2+\rho gh=p_2+\frac{1}{2}\rho {\upsilon }_2^2+\rho gh\text{or}{P}_2=P_1+\frac{1}{2}\rho ({\upsilon }_1^2-{\upsilon }_2^2)=p+\frac{1}{2}\rho \{{\upsilon }^2-(2\upsilon {)}^2\}=p-\frac{3}{2}\rho {\upsilon }^2$