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 $A_{1}$ 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, which of the following equations hold true ?

• A. $v_{2}^{2}-v_{1}^{2}=2gh$
• B. $v_{2}^{2}+v_{1}^{2}=2gh$
• C. $v_{2}^{2}-v_{1}^{2}=gh$
• D. $v_{2}^{2}+v_{1}^{2}=gh$

Answer 1

Answer: (A)

Let $\rho $ be density of liquid flowing in the tube.
$A_{1}v_{1}=A_{2}v_{2}$
$\frac{v_{1}}{v_{2}}=\frac{A_{1}}{A_{2}}$
According to Bernoulli's equation for horizontal flow of liquid.
$P_{1}+\frac{1}{2}\rho v_{1}^{2}=P_{2}+\frac{1}{2}\rho v_{2}^{2}$
$P_{1}-P_{2}=\frac{1}{2}\left(\rho v_{2}^{2} - v_{1}^{2}\right) \, \left(\right.\because P_{1}-P_{2}=h\rho g\left.\right)$
$v_{2}^{2}-v_{1}^{2}=2hg$