Question

(20 points) A water truck's tank has internal dimensions of 12 meters in length and 1 meters in diameter. If the truck's load of pure water is 70 percent of full capacity, how heavy is the load in pounds? Water's density is 62.4 lb/ft3 lbs In kilograms, what is the weight of the load if the truck carries liquid nitrogen instead of water? The liquid nitrogen's density is 0.808 g/ml. kg

Answer 1

The diameter of cross-section is 1 meter so that its radius is 1/2 meter.

The volume of the cylindrical tank ( assumed to be cylindrical as diameter of cross-section is given) is π(1/2)² * 12 = 3π cubic meters.

The tanker is 70 % full so that the volume of water in the tank is 0.7 * 3π = 2.1 π cubic meters = 2.1 *3.1416 = 6.59736 cubic meters (approximately).

Further, 1 meter = 3.28084 feet so that 1 cubic meter = (3.28084)³ cubic feet = 35.3147 cubic feet (approximately).

Hence, the volume of water in the tank = 6.59736*35.3147 cubic feet = 232.98379 cubic feet (approximately).

Since the density of water is 62.4 lb/ft³. hence the weight of water in the tank =62.4*232.98379 = 14538.19 lbs. (approximately).

Further, 1 lb = 0.453592 kg so that the weight of water in the tank = 14538.19*0.453592 = 6594.41kg. (approximately).

The weight of the load, if the truck carries liquid nitrogen instead of water, will be 6594.41*(0.808/1) = 5328.28 kg. ( as the density of water is 1 g/ml).