Question

Water flows through a horizontal tube as shown in figure. If the difference of heights of water column in the vertical tubes in $2cm,$ and the areas of cross-section at $A$ and $B$ are $4{cm}^2$ and $2{cm}^2$ respectively, find the rate of flow of water across any action

• A. $126cm/s$
• B. $136cm/s$
• C. $146cm/s$
• D. $156cm/s$

Answer 1

The correct option is C $146cm/s$

$\text{given,}h=2cm$

$A_1=4{cm}^2$

$A_2=2{cm}^2$

$Acc.\text{to}\text{Continuity theorem}$

$A_1{v}_1=A_2{v}_2$

$4\cdot v_1=2\cdot v_2$

$v_2=2v_1$

Acc.to Bernoullis theorem

$P_0+\rho gh+\frac{1}{2}\rho v_1^2=P_0+0+\frac{1}{2}\rho v_2^2$

$g\times 2+\frac{1}{2}{v}_1^2=\frac{4v_1^2}{2}$

$4000=3v_1^2$

$v_1=36.5cm/s$

rate of flow$=36.5\times 4$

$=146{cm}^3/s$

Answer:- $\left(C\right)$