A non-viscous fluid of density is flowing in a tube as shown in figure

Question

A non-viscous fluid of density $ρ$ is flowing in a tube as shown in figure. Area of section-(1) is double that of section-(2). Centre of mass of section-(2) is h height above the Centre of mass of section-(1) and level of water in tube-1 is 'h' height above that in tube-2. Then:

Smart Achievers · Accepted Answer

(2)

$Applying Bernoulli's equation from section-(1) and (2)$

$P_{1} + \frac{1}{2} ρ V_{1}^{2} + ρ g h_{1} = P_{2} + \frac{1}{2} ρ V_{2}^{2} + ρ g h_{2}$

$P_{1} + \frac{1}{2} ρ V^{2} + 0 = P_{2} + \frac{1}{2} ρ {(2 V)}^{2} + ρ g h$

$and P_{1} - P_{2} = ρ g (2 h)$

$Solving we get, V = \sqrt{\frac{2 g h}{3}}$

$(C) Work done by gravitation force per unit value W_{g} = decrease in gravitational$

$P T_{value} = ρ g h_{1} - ρ g_{2}$

$P T_{value} = ρ g h_{1} - ρ g h_{2}$

$W_{g r} = 0 - ρ g h$

$(D) Work done by elastic force volume, W_{e} = decrease in elastic P.E vol = decrease in pressure$

$E_{vol} = P_{1} - P_{2} = ρ G (2 h)$

Solution

Q.
A non-viscous fluid of density $ρ$ is flowing in a tube as shown in figure. Area of section-(1) is double that of section-(2). Centre of mass of section-(2) is h height above the Centre of mass of section-(1) and level of water in tube-1 is 'h' height above that in tube-2. Then:

1 Velocity of fluid of section-(1) is $\sqrt{\frac{g h}{3}}$

2 Velocity of fluid at section-(1) is $\sqrt{\frac{2 g h}{3}}$

3 Work done by gravitational force per unit volume from section-(1) to section-(2) is $ρ g h$

4 Work done by elastic forces (pressure) per unit volume from section-(1) to section-(2) is $3 ρ g h$

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Solution

Q. A non-viscous fluid of density ρ is flowing in a tube as shown in figure. Area of section-(1) is double that of section-(2). Centre of mass of section-(2) is h height above the Centre of mass of section-(1) and level of water in tube-1 is 'h' height above that in tube-2. Then:

1 Velocity of fluid of section-(1) is gh3

2 Velocity of fluid at section-(1) is 2gh3

3 Work done by gravitational force per unit volume from section-(1) to section-(2) is ρgh