Need help with fluids and pressure problem

[brett812718]

[SOLVED] need help with fluids and pressure problem

Homework Statement

The L-shaped tank shown below is filled with water and is open at the top.
(a) If d = 4.0 m, what is the force on face A due to the water?
N (up)

(b) What is the force on face B due to the water?
N (right)

Homework Equations

F=PA

The Attempt at a Solution

Fa=PaAa+Patmosphere
Pa=pgHa
Ha=2d
Fa=pg2d^3+Patmosphere
d=4
I got 2.85x10^6N but that was wrong
I was given this hint when i got it wrong:Can you find the pressure at a given depth? How is force related to pressure for a given horizontal surface area? On the vertical wall, how does pressure vary with depth along the wall? Do you see that you need to first consider a strip that has the wall's width but only a differential height dy? What is the force on the strip? Do you see that you next must integrate to find the force on the full wall (all the horizontal strips)?
is this how it should be done:
Fa=Integral(pgd^2 dy)+Patmosphere

 

[brett812718]

(a) If d = 4.0 m, what is the force on face A due to the water?
N (up)
i was not suppose to add the Patmosphere
Fa=1.25E6N

 

[Moetasim]

Fa=Integral(pgd^2 dy)+Patmosphere
Fa=pgd^3/2+Patmosphere
Fa=1000kg/m^3 * 9.8m/s^2 *4m^3/2+1atm
Fa=19.6*2m^2+1atm
Fa=39.2 N+1atm
Fa=39.2 N+101,325 N/m^2
Fa=101364.2 N (up)

Fb=PaAb+Patmosphere
Pa=pgHa
Ha=2d
Fb=pg2d^3+Patmosphere
d=4
Fb=101364.2 N (right)



Great job on using the correct equation (F=PA) to solve this problem! However, there are a few mistakes in your calculations.

Firstly, in part (a), you have used the incorrect value for the height (Ha). The height should be the vertical distance from the top of the tank to face A, which is equal to d. This means that the correct equation for Fa is Fa=pgd^2+Patmosphere.

Secondly, in part (b), you have used the incorrect value for the surface area (Ab). The surface area should be the area of face B, which is equal to d^2. This means that the correct equation for Fb is Fb=pgd^3+Patmosphere.

Finally, when solving for the force on face A, you have correctly used the hint to consider a differential height dy and then integrate to find the force on the full wall. However, in your calculation, you have used the incorrect limits for the integral. The correct limits should be from 0 to d, since the differential height dy starts at the bottom of the tank and goes up to the top.

After correcting these mistakes, the final answers should be:
(a) Fa=pgd^3/2+Patmosphere=101,364.2 N (up)
(b) Fb=pgd^3+Patmosphere=161,382.8 N (right)

Remember to always carefully consider the given information and use the correct equations and units to solve fluid and pressure problems. Keep up the good work!