Neglect air resistance and viscosity for the first 3 sub-questions. Take ac- cel

Question

Neglect air resistance and viscosity for the first 3 sub-questions. Take ac- celeration due to gravity, g = 10m/s2. (a) A liquid of mass 5.0 kg is in a jar held at a height of 2.0 m above the ground. Find the gravitational potential energy of the liquid in the jar (b) If the jar is slowly tilted so that the liquid is poured out of the jar, find the velocity of the liquid when it reaches the ground. (c) Find the time taken for the first particle of fluid to reach the ground from the instant it leaves the lip of the jar. (d) If the liquid in the jar is at room temperature, and right after pouring out of the jar it collects in a shallow puddle on the ground would you expect the temperature of the liquid in the puddle to be the same or different from when it was in the jar? Briefly explain your answer. (e) Would your answer to 2d above change if instead of being poured on the ground the liquid was poured into another container that rests on a vertical spring? Briefly explain your answer. 3. A large dam creates a reservoir of water that is maintained at a height of 150 m above a watershed area downstream of the dam. See figure 2. 120 m3/s of water flows down from the reservoir through a pipe and is used to drivea turbine-generator system to generate electricity. Because of losses in the piping system, only 80% of the total potential energy of the water is available to the turbine The turbine-generator systern has an efficiency of 90%. Estimate the power generated by the system. 5 points 4. Water at 20°C is siphoned fron a reservoir as shown in the figure 3. The siphon pipe has a constant diameter d -0.1/Vm, and is smooth so that viscous losses are small enough to be neglected. The pipe exit is at a height H-50 m below the water level in the tank. The center-line of the highest point of the ipe is at a beight h 2.0 m above the water level in the tank Assume the following values: density of water, ? 103 kg/m3 Atmospherie pressure, Patm -10 Pa Acceleration due to gravity,8-10 m/ (a) Find the velocity that the water exits from siphon pipe (b) Find the mass fow rate from the pipe

Explanation / Answer

2 a) Gravitational potential energy of the liquid in the jar = m.g.h = 5 . 10 . 2 = 100 Joules

b) Velocity of the liquid when it reaches the ground = sq. root (2 . g . h) = sq. root (2 .10. 2) = sq. root (40) = 6.32 m/s

c) Time taken for the liquid to reach the ground = sq. root (2. h / g) = sq. root (4/10) = sq. root (0.4) = 0.63 s

d) Since air resistance and viscosity is to be considered, the temperature of the liquid that reach the ground will surely be higher than that of the liquid in the jar as Potential Energy of the liquid in the jar will get converted into kinetic energy and some part of it will raise the temperature of the liquid.

e) At the instant when the liquid in the jar reaches the container that rests on a vertical spring, the temperature will definitely be higher as the temperature is raised due to air resistance and it will be available in both the cases irrespective of the place on which it is falling.

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