Question

The ocean liner Titanic lies under 12500 feet of water at the bottom of the Atlantic Ocean. (The density of water is 62.4 lb/ft3.)
(a) What is the water pressure at the Titanic? (Give your answer in both pounds per square foot and pounds per square inch.)
I got 780000 lbs/ft^2 which is equal to about 5416.67 lbs/in^2
(b) What is the total force on a circular porthole (window) of diameter 7 feet standing vertically with its center at the depth of the Titanic?

Answer 1

Answer:

a)$780000 lb/ft^2$

b)Total force = 30017917.805 lb

Step-by-step explanation:

Depth of titanic = 12500 feet

Density of water =$62.4 lb/ft^3$

a)Water pressure at the Titanic =$depth \times density = 12500 \times 62.4=780000 lb/ft^2$

b)

Set up a integral that gives a total force

Diameter = 7 feet

$Radius = \frac{7}{2}\\x^2+y^2=(\frac{7}{2})^2\\r^2+h^2=(\frac{7}{2})^2\\r=\sqrt{(\frac{7}{2})^2-h^2}$

Rectangular strip area =$2r \Delta h$

Pressure = 62.4(12500-h)

Force =$Pressure \times Area$

Force =$62.4(12500-h) \times 2(\sqrt{(\frac{7}{2})^2-h^2}) \Delta h$

Total force = $\int\limits^{\frac{7}{2}}_{\frac{-7}{2}} {124.8(12500-h)\sqrt{(\frac{7}{2})^2-h^2} \, dh$

Total force = 30017917.805 lb