You work at a facility that does pressurized tests. The things you test are very

Question

You work at a facility that does pressurized tests. The things you test are very heavy and need to be raised and lowered inside of the testing chamber using a hydraulic lift. The lift is shown in Figure 2. Suppose that you are testing an object that has a mass of 1000 kg. The diameter of the piston is 1.2 m, the pressure outside the chamber is 1 atm, the temperature is 20 degree C everywhere, and the liquid is engine oil. Suppose the pressure in the chamber is 1.25 times the pressure outside the chamber. How high h should the column of liquid be in order to raise the object? Suppose that the pressure in the chamber is reduced to 1 atm. How high h should the column of liquid be in order to raise the object? Suppose that the pressure in the chamber is 0.95 times the pressure outside the chamber. How high h should the column of liquid be in order to raise the object?

Explanation / Answer

Here ,

a) let the height is h

balancing the pressure in both sides

1000 * 9.8/(pi * (1.2/2)^2) + 1.25 * 1.01 *10^5 = 1.01 *10^5 + p * g * h

1000* 9.8/(pi * (1.2/2)^2) + 1.25 * 1.01 *10^5 = 1.01 *10^5 + 1000 * 9.8 * h

solving for h

h = 3.47 m

the height h is 3.47 m

b) for the pressure in the chamber to be 1 atm

1000* 9.8/(pi * (1.2/2)^2) + 1* 1.01 *10^5 = 1.01 *10^5 + p * g * h

1000* 9.8/(pi * (1.2/2)^2) + 1 * 1.01 *10^5 = 1.01 *10^5 + 1000 * 9.8 * h

h = 0.884 m

the height in the chamber is 0.884 m

c) for the pressure in chamber to be 0.95 times

1000* 9.8/(pi * (1.2/2)^2) + 0.95* 1.01 *10^5 = 1.01 *10^5 + p * g * h

1000* 9.8/(pi * (1.2/2)^2) + 0.95 * 1.01 *10^5 = 1.01 *10^5 + 1000 * 9.8 * h

solving for h

h = 0.369 m

the height of the liquid h is 0.369 m

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