Question about Calculus involving Titanic?

Question

I've been trying to do this problem but I keep getting answers that don't make sense:

The ocean liner Titanic lies under 12,500 feet of water at the bottom of the Atlantic Ocean.

Set up and calculate an integral giving the total force on a circular porthole (window) of diameter 6 feet standing vertically with its center at the depth of the Titanic.

This is what I came up with assuming that pressure of water is 62.4 lb/ft^3

i came up with the integral for total force on the slice to be:

the integral from 12497 to 12,503 of 124.8h*(9-h^2)

If someone could tell me where I'm wrong that would help out a lot

ps. I got 9-h^2 from doing pythagorean theorem where r^2+h^2=3^2
Then since that was the radius I multiplied it two for the formula of the area of each horizontal slice.

Answer 1

Pascal
(Pa)
Bar
(bar) Technical atmosphere
There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). Equation 1 is used when the value of standard temperature lapse rate is not equal to zero and equation 2 is used when standard temperature lapse rate equals zero.

Equation 1:

{P}=P_b \cdot \left[\frac{T_b}{T_b + L_b\cdot(h-h_b)}\right]^\frac{g_0 \cdot M}{R^* \cdot L_b}

Equation 2:

{P}=P_b \cdot \exp \left[\frac{-g_0 \cdot M \cdot (h-h_b)}{R^* \cdot T_b}\right]

where

P = Static pressure (pascals)
T = Standard temperature (kelvins)
L = Standard temperature lapse rate (kelvins per meter)
h = Height above sea level (meters)
R * = Universal gas constant for air: 8.31432×103 N·m / (kmol·K)
g0 = Gravitational constant (9.80665 m/s²)
M = Molar mass of Earth's air (28.9644 g/mol)

Or converted to English units:[3]

where

P = Static pressure (inches of mercury)
T = Standard temperature (kelvins)
L = Standard temperature lapse rate (kelvins per foot)
h = Height above sea level (feet)
R * = Universal gas constant (using feet and kelvins and gram moles: 8.9494596×104 kg·ft2·s-2·K-1·kmol-1)
g0 = Gravitational constant (32.17405 ft/s²)
M = Molar mass of Earth's air (28.9644 g/mol)

Average sea-level pressure is 1013.25 hPa (mbar) or 29.921 inches of mercury (inHg).
(at)
Atmosphere
(atm)
Torr
(mmHg) Pound-force per
square inch
(psi)
1 Pa ≡ 1 N/m² 10−5 10.197×10−6 9.8692×10−6 7.5006×10−3 145.04×10−6

Answer 2

I'm doing the same problem right now. If you posted, maybe we could exchange some thoughts and compare answers. What school do you go to?