"Calculate Resultant Force on Vertical Dam Wall

[etothey]

Homework Statement

Pressure_2.jpg: http://www.imageupload.org/thumb/thumb_8609.jpg
A vertical dam wall has a width w. Water is filled to a height H behind the dam. Calculate the resultant force on the dam wall.

Homework Equations

P=F/A
P= Pa + p*g*h

The Attempt at a Solution

Using picture to solve the question
P=F/A
A=H*W
Thus P=Pa g*h*p where p is density and P is pressure.
Thus F=P*A=H*W*(Pa + gHp) where g is gravity.

Is this correct?

 

[Metaleer]

Your solution, as I've understood it, would work if the pressure were uniform, that is, constant. However, it changes as you go down, so you would need to perform an integration to determine the net force.

 

[etothey]

Your solution, as I've understood it, would work if the pressure were uniform, that is, constant. However, it changes as you go down, so you would need to perform an integration to determine the net force.

Aha, I see. This is first fluid question I had involving integration.
Thus, I integrated $$\int$$Po + pgh dh from 0 to H.
Getting P=PaH + pgH^2/2.
Thus
PA = HW(PaH + pgH^2/2).
Better now?

 

[etothey]

anyone?

 

[rwisz]

I would like to first clarify a few things. In the given problem, we are assuming that the dam wall is a solid and impermeable structure. Also, we are assuming that the water pressure is constant throughout the entire height of the dam wall.

With that being said, your solution does seem to be correct. The resultant force on the dam wall would be equal to the pressure exerted by the water multiplied by the area of the dam wall, which is H*W in this case. The pressure can be calculated using the formula P=Pa+pgH, where Pa is the atmospheric pressure and pgH is the hydrostatic pressure due to the height of the water.

However, it is important to note that the units of pressure should be consistent. In your solution, the units for Pa and pgh are different (Pa is in N/m^2 while pgh is in N/m). It would be more accurate to use the same unit for both, such as using pgh in N/m^2.

Additionally, it would be beneficial to include the values for the given variables, such as the density of water and the acceleration due to gravity, in order to obtain a numerical value for the resultant force. Overall, your solution is on the right track and can be considered correct with some minor adjustments.