A liquid flows through a horizontal tube. The | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to the equation of continuity,the volume flow rate is constant: $A_1v_1 = A_2v_2$. Thus,option $(A)$ is correct.Applying Bernoulli's pri

Vedclass · Accepted Answer

${v_2} - {v_1} = \sqrt {2gh} $

Vedclass · Answer

(B) According to the equation of continuity,the volume flow rate is constant: $A_1v_1 = A_2v_2$. Thus,option $(A)$ is correct.Applying Bernoulli's principle for a horizontal tube $(h_1 = h_2)$: $P_1 + \frac{1}{2}ho v_1^2 = P_2 + \frac{1}{2}ho v_2^2$$P_1 - P_2 = \frac{1}{2}ho(v_2^2 - v_1^2)$Since the pressure difference is given by the height difference $h$ in the manometers,$P_1 - P_2 = ho gh$. Therefore,$ho gh = \frac{1}{2}ho(v_2^2 - v_1^2)$,which simplifies to $v_2^2 - v_1^2 = 2gh$. Thus,option $(C)$ is correct.Option $(B)$ states $v_2 - v_1 = \sqrt{2gh}$,which is mathematically incorrect because $\sqrt{v_2^2 - v_1^2} 
eq v_2 - v_1$.Option $(D)$ is incorrect because,in a real fluid flow,energy is dissipated due to viscosity,and even in an ideal fluid,the total energy per unit mass (Bernoulli's constant) is conserved,but the distribution between pressure energy and kinetic energy changes. However,in the context of this specific question,option $(B)$ is the most explicitly incorrect mathematical statement.

$A$ liquid flows 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 $h$. The incorrect statement is

Similar Questions

Give the formula for the measurement of the velocity of a fluid in the broader part of a venturi-meter.

Water flows through the tube shown. The cross-sectional areas of the wide and narrow parts are $5 \text{ cm}^2$ and $2 \text{ cm}^2$,respectively. The rate of flow is $500 \text{ cm}^3/\text{s}$. Find the difference in the mercury level of the $U$-tube in $\text{cm}$.

Why do two rowing boats moving parallel to each other come closer (attract) to each other?

Vedclass Test Series

Exam Paper Generator

Online Exam Module