A liquid flows through a horizontal tube as shown in figure. The velocities of the liquid in the two sections, which have areas of cross-section A1 and A2 , are v1 and v2 , respectively. The difference in the levels of the liquid in the two vertical tubes is h . Then, which of the following equations hold true ?

Question

A liquid flows through a horizontal tube as shown in figure. The velocities of the liquid in the two sections, which have areas of cross-section A1 and A2 , are v1 and v2 , respectively. The difference in the levels of the liquid in the two vertical tubes is h . Then, which of the following equations hold true ? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-cf5qttfamyfqz8pc.jpg" /> (A) v22-v12=2gh (B) v22+v12=2gh (C) v22-v12=gh (D) v22+v12=gh

Tardigrade Admin · Accepted Answer

Let ρ be density of liquid flowing in the tube. A1v1=A2v2 (v1/v2)=(A1/A2) According to Bernoulli's equation for horizontal flow of liquid. P1+(1/2)ρ v12=P2+(1/2)ρ v22 P1-P2=(1/2)(ρ v22 - v12) (.∵ P1-P2=hρ g.) v22-v12=2hg

$v_{2}^{2} - v_{1}^{2} = 2 g h$

$v_{2}^{2} + v_{1}^{2} = 2 g h$

$v_{2}^{2} - v_{1}^{2} = g h$

$v_{2}^{2} + v_{1}^{2} = g h$

v22​−v12​=2gh

v22​+v12​=2gh

v22​−v12​=gh

v22​+v12​=gh

Let ρ be density of liquid flowing in the tube. A1​v1​=A2​v2​ v2​v1​​=A2​A1​​ According to Bernoulli's equation for horizontal flow of liquid. P1​+21​ρv12​=P2​+21​ρv22​ P1​−P2​=21​(ρv22​−v12​)(∵P1​−P2​=hρg) v22​−v12​=2hg

$v_{2}^{2} - v_{1}^{2} = 2 g h$

$v_{2}^{2} + v_{1}^{2} = 2 g h$

$v_{2}^{2} - v_{1}^{2} = g h$

$v_{2}^{2} + v_{1}^{2} = g h$