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Q.

The diagram shows venturimeter through which water is flowing. The speed of water at X is 2 cm/s. Find the speed of water at Y in cm/s. (taking g=1000 cm/ $s^{2}$ ).

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answer is 32.

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Detailed Solution

Applying Bernoulli equation,

$P_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{1} + \frac{1}{2} ρ v_{2}^{2}$

$\Rightarrow \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2}) = P_{1} - P_{2} = h g ρ$

$\Rightarrow v_{2}^{2} = v_{1}^{2} + 2 g h$

$\Rightarrow v_{2} = \sqrt{v_{1}^{2} + 2 g h} = \sqrt{2^{2} + 2 \times 1000 \times 0.51} = \sqrt{1024} = 32 c m / s$

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The diagram shows venturimeter through which water is flowing. The speed of water at X is 2 cm/s. Find the speed of water at Y in cm/s. (taking g=1000 cm/s2).