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Standard XII

Physics

Bernoulli's Principle

A smooth pipe...

Question

A smooth pipe of diameter 200mm carries water. The pressure in the pipe at section S1 (elevation: 12m) the pressure is 20kPa and velocity is $2 m s^{- 1}$ . Density of water is $1000 k g m^{- 3}$ and acceleration due to gravity is $9.8 m s^{- 2} .$ Which of the following is TRUE?

flow from S1 to S2 and head loss is 0.53m

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flow from S2 to S1 and loss is 0.53m

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flpow from S1 to S2 and head loss is 1.06m

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flow from S2 to S1 and head loss is 0.06m

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Solution

The correct option is C flpow from S1 to S2 and head loss is 1.06m
Assuming flow from $S_{1}$ to $S_{2}$ -

$h_{1} = \frac{p_{1} - p_{2}}{p g} + \frac{{v_{1}}^{2} - {v_{2}}^{2}}{2 g} + z_{1} = z_{2}$

But for continuity equation for incompressible fluids

$A_{1} v_{1} = A_{2} v_{2} & A_{1} = A_{2}$

$v = v_{2}$

$h_{1} = \frac{p_{1} - p_{2}}{p g} + z_{1} - z_{2}$

$h_{1} = 1.06 m (+ v e)$

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A smooth pipe of diameter 200mm carries water. The pressure in the pipe at section S1 (elevation: 12m) the pressure is 20kPa and velocity is 2ms−1. Density of water is 1000kgm−3 and acceleration due to gravity is 9.8ms−2. Which of the following is TRUE?

The correct option is C flpow from S1 to S2 and head loss is 1.06mAssuming flow from S1 to S2 - h1=p1−p2pg+v12−v222g+z1=z2 But for continuity equation for incompressible fluids A1v1=A2v2&A1=A2 v=v2 h1=p1−p2pg+z1−z2 h1=1.06m(+ve)

A smooth pipe of diameter 200mm carries water. The pressure in the pipe at section S1 (elevation: 12m) the pressure is 20kPa and velocity is $2 m s^{- 1}$ . Density of water is $1000 k g m^{- 3}$ and acceleration due to gravity is $9.8 m s^{- 2} .$ Which of the following is TRUE?