# Triple integrals and power calculation for a piston?

Question Details:

This is not a thermodynamics problem, it should be solved using advanced calculus methods.

Consider the piston-cylinder arrangement shown in the figure below. The

cylinder has a diameter equal to 10 m. Water enters radially the flow domain (space

between the piston and the cylinder) from the left quarter of the periphery with a velocity V1 = 2 m/s and leaves from the other (right) quarter with V2 = 2 m/s. The inlet A1 and outlet A2 areas are 1 m2 and 2 m2 respectively. The density of water ρ is considered to be constant and equal to 1000 kg/m3. Calculate the velocity of the piston (use a vectorial representation). What is the power required to raise the piston against gravity if the piston’s mass is 500 kg? (The conventional standard value for the gravitational acceleration is 9.80665 m/s2)

Use the law of conservation of mass in integral form:

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Variable β represents the instantaneous volume of the flow domain, N is a unit vector normal and away from the surface, and the rest of the variables assume their usual meaning. Each term in the above equation has the units of mass/time [in SI system: kg/s]

### 2 Answers

- detherowLv 43 years ago
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