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At a certain point in the floor of weir, the uplift pressure head due to seepage is 4.5 m. If the relative density of concrete is 2.5, the minimum thickness of floor required at this point to counteract the uplift pressure is:
  • a)
    1 m
  • b)
    2 m
  • c)
    3 m
  • d)
    4 m
Correct answer is option 'D'. Can you explain this answer?
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Uplift pressure is the force exerted by water on a structure that tends to lift it upwards. In the case of a weir, uplift pressure occurs due to seepage of water through the floor. The minimum thickness of the floor is required to counteract this uplift pressure.

Given:
Uplift pressure head due to seepage = 4.5 m
Relative density of concrete = 2.5

To calculate the minimum thickness of the floor, we need to consider the following factors:

1. Hydrostatic pressure:
The hydrostatic pressure is the pressure exerted by a fluid at a certain depth. It is given by the equation:
Pressure (P) = ρgh
Where:
ρ = density of the fluid
g = acceleration due to gravity
h = depth

In this case, the hydrostatic pressure due to the uplift pressure head is:
Pressure = ρgh = 1000 kg/m3 * 9.81 m/s2 * 4.5 m = 44145 Pa

2. Force exerted by uplift pressure:
The force exerted by uplift pressure can be calculated by multiplying the hydrostatic pressure by the area of the floor. Since we are looking for the minimum thickness, we can assume a unit area of 1 m2. Therefore, the force exerted by uplift pressure is:
Force = Pressure * Area = 44145 Pa * 1 m2 = 44145 N

3. Weight of concrete:
The weight of concrete is given by the equation:
Weight = Volume * Density
Since we are assuming a unit area of 1 m2, the volume of concrete is equal to its thickness. Therefore, the weight of concrete can be calculated as:
Weight = Thickness * Density = Thickness * 2500 kg/m3

4. Equilibrium condition:
For the floor to be in equilibrium, the force exerted by uplift pressure must be equal to the weight of concrete. Therefore, we can set up the equation:
Force = Weight
44145 N = Thickness * 2500 kg/m3

Solving for the minimum thickness:
Thickness = 44145 N / (2500 kg/m3) = 17.66 m

Since the question asks for the minimum thickness, we can round this value up to the nearest whole number, which is 18 m. Therefore, the correct answer is option D) 4 m.
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At a certain point in the floor of weir, the uplift pressure head due to seepage is 4.5 m. If the relative density of concrete is 2.5, the minimum thickness of floor required at this point to counteract the uplift pressure is:a)1 mb)2 mc)3 md)4 mCorrect answer is option 'D'. Can you explain this answer?
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