Question

A liquid flow through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross section $A_1$ and $A_2$ are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$. Then

• A. The volume of the liquid flowing through the tube in unit time is $A_1$ $v_1$
• B. $v_2-v_1=\sqrt{2gh}$
• C. $v_2^2-v_1^2=2gh$
• D. The energy per unit mass of the liquid is the same in both section of the tube

Answer 1

Answer: (A), (C), (D)

The correct options are
A The volume of the liquid flowing through the tube in unit time is $A_1$ $v_1$
C $v_2^2-v_1^2=2gh$
D The energy per unit mass of the liquid is the same in both section of the tube

According to Bernoulli's principle

$h\rho g=\frac{1}{2}\rho (v_2^2-v_1^2)\Rightarrow v_2^2-v_1^2=2gh$

Volume of liquid flowing in unit time$=\frac{volume}{sec}=A_1{v}_1=A_1\frac{dx}{df}$

According to conservation of energy (Bernoulli's principle) and equation of continuity (conservation of mass)

Energy per unit mass of liquid is same in both section.