A sealed tank has 2-openings as shown below. One at near top and other at near bottom. Let height of water filled above the bottom opening is h and a compressor producing a pressure p is connected to top opening. Velocity of water obtained from lower opening is (take, atmospheric pressure pa such that .p-pa=ρ g h)

Question

A sealed tank has 2-openings as shown below. One at near top and other at near bottom. Let height of water filled above the bottom opening is h and a compressor producing a pressure p is connected to top opening. Velocity of water obtained from lower opening is (take, atmospheric pressure pa such that .p-pa=ρ g h) (A) √2 g h (B) √g h (C) 2 √g h (D) 0

Tardigrade Admin · Accepted Answer

Applying Bernoulli's theorem, at different parts of figure given below,

p_{a} + \frac{1}{2} ρ v_{1}^{2} + ρ g y_{1} = p + \frac{1}{2} ρ v_{2}^{2} + ρ g y_{2}

= p + ρ g y_{2} [∵ v_{2} = 0]

v_{1}^{2} = \frac{2}{ρ} (p - p_{a} + ρ g (y_{2} - y_{1})) .... (i)

Given,

y_{2} - y_{1} = h

Substituting the given value in Eq. (i), we get

v_{1} = 2 g h + \frac{2 ( p - p _{a} )}{ρ}

= 2 g h + \frac{2 ( ρ g h )}{ρ} = 2 g h

$2 g h$

$g h$

$2 g h$

$0$

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$2 g h$

$g h$

$2 g h$

$0$