Question

Water is poured in a tank through a cylindrical tube of area of cross section $A$ and ejecting water at a constant speed $4m/s$. The tank contains a hole of area $A/2$ at bottom. Level of water in the tank will not go up beyond $take(g=10m/s)$

• A. $5.6m$
• B. $4.8m$
• C. $3.2m$
• D. $1.8m$

Answer 1

The correct option is C $3.2m$

According to bernoulli's theo rem

$P_0+\rho gH+\frac{1}{2}\rho v_1^2=P_0+0+\frac{1}{2}\rho v_2^2$ (tor max. height H)

$\Rightarrow gH+\frac{v_1^2}{2}=\frac{v_2^2}{2}$

According to Equation of continuity

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

$A\times 4=\frac{A}{2}X{v}_L\Rightarrow v_2=8ms$

Now

$gH+\frac{u^2}{2}=\frac{8^2}{2}\Rightarrow 10\times H=\frac{64-16}{2}\Rightarrow 2.4m$

So, Height More than $2.4M$ is Requined Answer (c) $3.2m$.