# Calculus - Hydrostatic Pressure

posted by .

Find the hydrostatic pressure on one end of a water trough full of water, the end of which is a trapezoid with given dimensions: top of trapezoid = 20 feet, sides of trapezoid both = 8 feet, bottom of trapezoid = 12 feet.

Depth of water = 8 feet
Density of water = 62.4 lb/ft^3
gravity = 32.15 ft/s^2

a/(8-xi*) = (4ft)/(8ft)
a = (8-xi*)/2 = 4 - (xi/2)
Wi = 2(6+a) = 2(6+4-(1/2)xi*)=20 - xi*
Ai = Wi*delta x = (20-xi*)delta x
Pi = rho*g*d
Pi = (62.4 lb/ft^3)(32.15 ft/s^2)xi
Fi = Pi*Ai
Fi = (62.4 b/ft^3)(32.1/s^2)xi*(20-xi*) delta x
Fi = Integral from 0 to 8 of:
(62.4)(32.15)x(20-x)dx
Fi = 2006.16*Integral 0 to 8 of: (20x-x^2)dx
=2006.16[10x^2-(x^3)/3] evaluated at 0 and 8
=9.42 x 10^5 (what are the units here? lb/(ft^3*s^2)???

Your density of water in lbs/ft^3 is the weight of water at sea level. It is not mass density. So no need to multiply by 32 ft/sec to turn into a force. That is one error.

also, your depth is wrong. If the slanted sides are 8 ft, the depth is about six feet.

• Calculus - Hydrostatic Pressure -

• Calculus - Hydrostatic Pressure -

16049.28

## Similar Questions

1. ### College Physiology

At the venular end of the capillary, the hydrostatic pressure is?
2. ### anatomy&physiology

What directions glomerular hydrostatic pressure,capsule hydrostatic pressure and blood colloid osmotic pressure will cause fluid to move.I've tried to look on internet differen imformations but just don't get it.Thank you for your …
3. ### calculus

A trough is 10 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x10 from x=−1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds required …
4. ### Calculus (Definite Integrals - Fluid Pressure)

The ends of a water trough have the shape of the region bounded by the graphs of y = x2 and y = 4 with x and y both measured in feet. To what depth must the trough be filled with water so that the force exerted by the water on either …
5. ### Calculus

A trough is 3 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of x^2 from -1 to 1 . The trough is full of water. Find the amount of work required to empty the trough by …
6. ### math

A water trough is 4 m long and its cross-section is an isosceles trapezoid which is 210 cm wide at the bottom and 280 cm wide at the top, and the height is 70 cm. The trough is not full. Give an expression for V, the volume of water …
7. ### calculus

A water-trough is 10m long and has a cross-section which is the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has height 50cm. If the trough is being fi lled with water at the rate of 0.2 …