Fluid Pressure, YAY!

[Guest]

Hello, I'm just finishing some problems and I got stuck on two of them... I know I have to use an integral to solve them (Yay, integrals! ) But I keep getting stuck. Any help's appreciated, as always! Thanks in advance.

24) A water trough 10 ft long has a square cross section that is 2 ft wide. If the trough is full of water (density p=62.4lb/ft^3), find the force exerted by the water on one end of the trough.


56) A cylindrical tank 8 ft in diameter is lying on its side and is half full of oil of density p=75 lb/ft^3. Find the total force F exerted by the oil on one end of the tank.

 

[skeeter]

\(\displaystyle \L F = w \int_c^d h(y) \cdot L(y) dy\)

where w is the weight density of the fluid

h(y) is the depth of a representative horizontal "slab" of fluid in terms of y

L(y) is the horizontal length of the representative horizontal "slab" of fluid in terms of y

24) let the bottom of the trough be y = 0 ...
\(\displaystyle \L F = 62.4 \int_0^2 y \cdot 2 dy\)

56) let the center of the circular side be the origin ...

\(\displaystyle \L F = 75 \int_{-4}^0 -y \cdot 2\sqrt{16-y^2} dy\)

 

[Guest]

Thanks!

Thanks for your help... when I solved the integrals (it really helped to draw pictures, the diagrams helped me see where the equations came from!) and I found the first one to be 249.6N and the second one was 3200N.

Thanks!