I have a question on fluids.
Water in a section 1.2m wide, 2m high. retained by sluice gate that can pivot about its base.
There is a retaining cable at the top of the gate. Determine tension in the retaining cable at the top of the gate when the depth of water is 1.8m. Density of water is 1020 kg/m3.
Is this to do with hydrostatic pressure?
So work out area of section: 1.2m x 2m = 2.4 m2
Then F = pAgh
= 1020 x 2.4 x 9.81 x 1.8
=43.23 kPa or NM
Yes, this question is related to hydrostatic pressure. To determine the tension in the retaining cable at the top of the gate, you need to calculate the hydrostatic pressure due to the depth of the water.
First, calculate the area of the section by multiplying the width (1.2m) by the height (2m): Area = 1.2m x 2m = 2.4m^2.
Next, you can use the hydrostatic pressure formula: P = ρgh, where P is the pressure, ρ is the density of the fluid (in this case, water with a density of 1020 kg/m^3), g is the acceleration due to gravity (9.81 m/s^2), and h is the depth of the water (1.8m).
Plugging in the values, the hydrostatic pressure is calculated as follows:
P = 1020 kg/m^3 x 9.81 m/s^2 x 1.8m = 17766.12 N/m^2 or 17.77 kPa.
Since the hydrostatic pressure is acting in a vertical downward direction, the tension in the retaining cable at the top of the gate must be equal to the hydrostatic pressure to maintain equilibrium. Therefore, the tension in the retaining cable is 17.77 kPa or 17766.12 N/m^2.