A long cylindrical tank of radius 1m is being filled by a pipe of radius $2 c m .$ The incoming water has a velocity of $1 m / s$ . The tank has a hole of radius $1 c m$ at the bottom. lf the height of water in the tank in steady state is $\frac{4 x}{5} m$ , find the value of $x$ ?

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Solution

for steady state
rate of inflow of water= rate of outflow of water
$a_{1} v_{1} = a_{2} v_{2}$
$\Rightarrow π (0.02)^{2} \times 1 = π (0.01)^{2} \sqrt{2 g h)} ∵$ velocity of efflux at depth h is given by $v = \sqrt{2 g h}$
$\Rightarrow 4 = \sqrt{2 \times 10 \times (\frac{4 x}{5})}$
$\Rightarrow x = 1$

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A long cylindrical tank of radius 1m is being filled by a pipe of radius 2cm. The incoming water has a velocity of 1m/s. The tank has a hole of radius 1cm at the bottom. lf the height of water in the tank in steady state is 4x5m, find the value of x ?

for steady state rate of inflow of water= rate of outflow of watera1v1=a2v2⇒π(0.02)2×1=π(0.01)2√2gh)∵ velocity of efflux at depth h is given by v=√2gh⇒4=√2×10×(4x5)⇒x=1

A long cylindrical tank of radius 1m is being filled by a pipe of radius $2 c m .$ The incoming water has a velocity of $1 m / s$ . The tank has a hole of radius $1 c m$ at the bottom. lf the height of water in the tank in steady state is $\frac{4 x}{5} m$ , find the value of $x$ ?