1. A cylindrical storage tank, with dimensions of 15 m height and 15 m inside di

Question

1. A cylindrical storage tank, with dimensions of 15 m height and 15 m inside diameter, is used to store oil having a specific gravity of 0.93 at 20 oC. The level of oil in the tank is determined by measuring the pressure in the tank using a pressure gauge that is 2 feet above the bottom of the tank. Assume that the pressure in the air space above the oil is maintained at atmospheric pressure. a.) Write an equation for the height of oil in the tank (in m) as a function of the pressure measured by the pressure gauge (in kPa). b.) Convert the equation from part a) so that the mass of oil (in kg) is given as a function of the measured pressure (in mmHg). c.) Using these equations, determine the height of oil and mass of oil when the pressure gauge reads 70 kPa.

Explanation / Answer

Pressure gauge is at 2 ft above the botttom...coverting it to SI units...
d =2ft = 0.6096 m

So pressure measured in the pressure gauge, P(in kPa) = g(h - 0.6096) / 1000

Here specific gravity is given...so... = 1000 * specific gravity = 930

SO, if P(in kPa) = *g*(h - 0.6096)

So, h = [P / 9.1233] + 0.6096

Now, pressure is given in mmHg

So, 1 kPa = 7.5 mmHg

So, P Kpa = 7.5*P mmHg

So, h = 0.822 P + 0.6096

So, V = * (15/2)^2 * h

m = V = 930 * * (15/2)^2 * h

m = 164344 (0.822 P + 0.6096)

When P = 70 kPa,

h = 8.28 m

m = 1361144.8 kg

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