4.60 × 105 gallons of turpentine (SG = 0.863) is stored in a 23.0-ft tall storag

Question

4.60 × 105 gallons of turpentine (SG = 0.863) is stored in a 23.0-ft tall storage tank. What is the pressure at the bottom of the tank in lbf/in^2 ?

4.60 x105 gallons of turpentine (SG 0.863) is stored in a 23.0-ft tall storage tank. What is the total mass of the liquid in the tank? Number .31x10 lb. What is the pressure at the bottom of the tank? Incorrect. The pressure at the bottom of the tank is equal to the pressure above the liquid level (since the tank is not pressurized, this is Number lb, inal to the a lb,/inequal to the atmospheric pressure) plus the hydrostatic pressure 638 Pay attention to the unit conversions during the hydrostatic pressure conversion. The density of turpentine is given in terms of pounds-mass but the pressure is in terms of pounds-force, so it is necessary to convert between the two units by dividing by 2.174 Ib. ft/s 1 lb Remember to convert between feet squared and inches squared, and that g 32.174 ft/s2

Explanation / Answer

Given, specific gravity of turpentine = 0.863

So, density of turpentine, d = 0.863 g / cm3

d = (0.863 g / cm3) * (1lb / 453.592g) * (3785.41 cm3 / 1 gallon)

since, 1lb = 453.592g    and 1 gallon = 3785.41 cm3

So, d = 7.202 lb / gallon

Given, volume, V = 4.6 * 105 gallon

Mass, m = d * V = 7.202 * 4.6 * 105 = 3.313 * 106 lbm

Hence, mass of turpentine = 3.313 * 106 lbm

Pressure at the bottom of the tank due to turpentine, P = d * g * h

where d = density = 7.202 lb / gallon = (7.202 lb / gallon) * (1 gallon / 0.13368 ft3)

since, 1 gallon = 0.13368 ft3

So d = 53.8749 lb / ft3

g = acceleration due to gravity = 32.174 ft / s2 ; h = height of liquid column = 23 ft (given)

So, Pressure at the bottom of the tank due to turpentine, P = d * g * h

P = 53.8749 * 32.174 * 23 = 39867.533 lbm / ft. s2

But we need pressure in units of lbf / in2

One pound force = 1lbf = 1 lbm * g      where g = acceleration due to gravity = 32.174 ft / s2

1lbf = 32.174 lbm ft / s2 = (32.174 lbm ft / s2) * (12in / 1ft) = 386.088 lbm in / s2

(since, 1ft = 12 inch)

So 1lbf = 386.088 lbm in / s2 and hence 1lbf / in2 = 386.088 lbm / in. s2

We have P = 39867.533 lbm / ft. s2 = (39867.533 lbm / ft. s2) * (1ft / 12 in)

Therefore, P = 3322.294 lbm / in. s2

P = (3322.294 lbm / in. s2) * { (1lbf / in2) / (386.088 lbm / in. s2 ) } = 8.605 lbf / in2

(since, 1lbf / in2 = 386.088 lbm / in. s2)

Therefore, pressure due to turpentine is P = 8.605 lbf / in2

Total pressure at bottom of tank = Patm + P

where Patm is atmospheric pressure = 14.7 lbf / in2

So total pressure at bottom of tank = 14.7 + 8.605 = 23.3 lbf / in2

So total pressure at bottom of tank = 23.3 lbf / in2

mass of turpentine = 3.313 * 106 lbm

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