Fluid dynamics

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Question

If water flows horizontally through a pipe of varying cross section and the pressure of water equals 10 cm of Hg at a point where the velocity of flow is 40 cm/s, What is the pressure at another point where the velocity of flow is 50 cm/s ? Take $g = 10 m / s^{2}$ .

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Solution

By Bernoulli's equation
$p_{2} + \frac{1}{2} ρ {v_{2}}^{2} = p_{1} + \frac{1}{2} ρ {v_{1}}^{2}$
$\Rightarrow ρ {gh}_{2} = ρ {gh}_{1} + \frac{1}{2} ρ ({v_{1}}^{2} - {v_{2}}^{2})$
$\Rightarrow h_{2} = h_{1} + \frac{{v_{1}}^{2} - {v_{2}}^{2}}{2 g} = 10 + \frac{40^{2} - 50^{2}}{2 x 1000} cm = 9.55 cm$

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Fluid dynamics

Remember concepts with our Masterclasses.

If water flows horizontally through a pipe of varying cross section and the pressure of water equals 10 cm of Hg at a point where the velocity of flow is 40 cm/s, What is the pressure at another point where the velocity of flow is 50 cm/s ? Take g = 10 m/s2.

By Bernoulli's equation p2+12ρv22=p1+12ρv12⇒ρgh2=ρgh1+12ρ(v12-v22)⇒h2=h1+v12-v222g=10+402-5022 x 1000cm=9.55 cm

Ready to Test Your Skills?

free study material

If water flows horizontally through a pipe of varying cross section and the pressure of water equals 10 cm of Hg at a point where the velocity of flow is 40 cm/s, What is the pressure at another point where the velocity of flow is 50 cm/s ? Take $g = 10 m / s^{2}$ .