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1. With an inner diameter of 0.3 mm, Fluid 1 is air, Fluid 2 is mercury, and Fluid 3 is water, all at 20°C. Point A is open to the standard atmosphere, whereas point B is at an elevation \( Z_B = 988 \) mm if \( Z_C = 743 \) mm and \( Z_D = 345 \) mm. Determine the absolute water pressure at point B. Compute all capillary actions and apply them to your results.

2. If the air pressure at sea level is 101.325 kPa and the density of air is 1.2 kg/m\(^3\):

a. Calculate the thickness of the atmosphere (m) above the earth.

b. What gauge pressure is experienced by a driver at a depth of 10 m in seawater with a relative density of 1.025? Assume \( g = 9.81 \) m/s\(^2\).

3. Two pistons connected by a pipe are filled with oil. The larger piston has a diameter of 3.2 ft and has a force of 763 lb applied to it. What is the diameter of the smaller piston if it can support a force of 27 lb?

4. Oil (SG = 0.93) is pumped from a well. If the pump is 11.7 ft above the surface of the oil, what pressure must the pump be able to generate to lift the oil up to the pump?

5. In the calibration of gauges in a factory, the quality assurance department uses a dead-weight tester. Weights loaded onto the piston carrier generate a known pressure in the piston cylinder, which in turn generates a reading on the gauge. If a pressure of 35 MPa is generated by the tester when loaded with a 100 kg weight, determine:

i. The diameter of the piston cylinder (mm).

ii. The load (kg) needed to produce a pressure of 150 MPa.

Answer :

The absolute water pressure at point B, considering capillary actions, is determined to be 988 mm + 2.696 mm + 11.75 mm = 1002.446 mm of water.

At the given elevation ZB = 988 mm, we need to account for the capillary actions due to the inner diameter of 0.3 mm. Capillary rise in a tube can be calculated using the formula h = 2T cosθ / ρrg, where h is the capillary rise, T is the surface tension, θ is the contact angle, ρ is the density of the fluid, r is the radius of the tube, and g is the acceleration due to gravity.

For fluid 2 (mercury) with higher surface tension, the capillary rise (2.696 mm) should be subtracted from the elevation, while for fluid 3 (water) with lower surface tension, the capillary rise (11.75 mm) should be added.

The absolute pressure at point B is given by the hydrostatic pressure equation P = ρgh, where ρ is the fluid density, g is the acceleration due to gravity, and h is the height difference.

In the case of air at point A, it's open to the atmosphere, so its pressure is the atmospheric pressure (101.325 kPa).

To calculate the thickness of the atmosphere, we use the hydrostatic pressure formula and rearrange it to solve for h, considering the air density and the atmospheric pressure.

For the gauge pressure experienced by a driver at a depth of 10 m in seawater, we use the hydrostatic pressure equation with the given relative density of seawater.

For the piston problem, we can use the principle of hydraulic systems, where pressure is transmitted equally. The force on each piston is given by the product of pressure and piston area. Equating the forces on the two pistons gives the ratio of their areas, and we can then calculate the diameter of the smaller piston.

In the case of pumping oil from a well, we need to consider the pressure required to lift the oil to the pump's height. This pressure is a function of the oil's density, the pump's height, and gravity.

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