Question

A Bathtub has dimensions of 5ft Long, 3ft wide, and 2ft tall. The tub itself weighs 300lbf. The tub contains 100 gallons of water at T-110°F. A human weighing 200lbs sits down in the tub. a. What is the volume of water in ft? 1. Grab a fluids text or find a table of specific weight of water in "English units" with temperature (It's NOT 62.4lbf/ft'), and find the weight of the water in units of Ibf. What is the total weight of tub plus human plus water? What is the pressure on the floor in units of psi (Ibf/in2)? b. c. d.

Answer 1

a) What is the volume of water in ft?

We are given that The tub contains 100 gallons of water

`1 UK gallon = 0.1605437 ft^3`

So,

`100 UK gallon = 100 * 0.1605437 = 16.05437ft`

b)Find the weight of the water in units of Ibf.

Specific weight of water at 100° F =
`61.862 lbf /ft^3`

Weight of water =
`61.862 * 16.05437 lbf = 993.15543694 lbf`

c)What is the total weight of tub plus human plus water?

Total weight = Weight of tub + weight of human + weight of water

`= 300 lbf + 993.155 lbf + 200 lbf = 1493.155 lbsf`

d)What is the pressure on the floor in units of psi (Ibf/in2)?

1 feet = 12 inches

Area of floor =
`5ft * 3ft = 5 * 12* 3 * 12 =60 in * 36in = 2160 in^2`

Pressure =
`\frac{\text{Total weight}}{Area} = (1493.155)/(2160) lbf /in^2=0.691 psi`

Hence the pressure is 0.691 psi