Lateral Force and Pressure on a dam

[designer rose]

1a. What is the total lateral force on a vertical dam 75 ft high and 135 ft wide if the water comes up to the very top of the dam?

I think I got the answer to this one, is it 2.4 x 10^7?

1b. What is the pressure on the lake bottom next to the dam?

 

[Q_Goest]

Show how you got 1a please.

If you got 1a, then how did you resolve the pressure distribution across the face of the dam?

 

[baba89]

To determine the total lateral force on a vertical dam, we first need to calculate the hydrostatic pressure of the water at the top of the dam. This can be done using the formula P = ρgh, where P is the pressure in Pascals, ρ is the density of water (1000 kg/m^3), g is the gravitational acceleration (9.8 m/s^2), and h is the height of the water column.

In this case, the height of the water column is equal to the height of the dam, which is 75 ft or 22.86 m. Plugging in these values, we get P = (1000 kg/m^3)(9.8 m/s^2)(22.86 m) = 2.18 x 10^5 Pa.

Next, we need to calculate the total lateral force on the dam. This can be done using the formula F = P*A, where F is the force in Newtons, P is the pressure in Pascals, and A is the area of the dam.

In this case, the area of the dam is 135 ft x 75 ft = 10125 ft^2. Converting to square meters, we get A = 942.73 m^2. Plugging in the values, we get F = (2.18 x 10^5 Pa)(942.73 m^2) = 2.05 x 10^8 N.

For the pressure on the lake bottom next to the dam, we can use the same formula P = ρgh, but this time the height of the water column is equal to the height of the dam plus the depth of the lake. Without knowing the depth of the lake, we cannot calculate the exact pressure. However, we can estimate it by assuming a depth of 100 ft or 30.48 m.

Using the same formula, we get P = (1000 kg/m^3)(9.8 m/s^2)(30.48 m) = 2.98 x 10^5 Pa. This is the pressure at the bottom of the lake next to the dam. Keep in mind that this is just an estimate and the actual pressure may vary depending on the depth of the lake.