The water level in a dam is 10 m. The total force acting on vertical wall per metre length is:a)49.05 kNb)490.5 kNc)981 kNd)490 kNCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Concept:
Whenever a static mass of fluid comes into contact with a surface the fluid exerts force upon that surface. The magnitude of this force is known as the hydrostatic force or total pressure force.
The magnitude of hydrostatic force is given by F = ρgh̅A
Where ρ = Density of the fluid, h̅ = Depth of center of gravity of the surface from free liquid surface, A = Area of the surface
Calculation:

Given, h = 10 m
h̅ = 10/2 = 5 m
Area per metre length = 10 × 1 = 10 m²
Force acting on vertical wall = ρ × g × h̅ × A
= 1000 × 9.81 × 5 × 10
= 490500 N
= 490.5 kN

Answer

Given:
Water level in the dam = 10 m

To find:
Total force acting on vertical wall per metre length

Solution:
The total force acting on the vertical wall of the dam is the product of the pressure exerted by the water and the area of the wall.

1. Pressure exerted by the water:
The pressure exerted by a fluid depends on its density and the depth of the fluid column. The pressure at a certain depth in a fluid can be calculated using the equation:

P = ρgh

Where:
P = pressure (N/m² or Pa)
ρ = density of the fluid (kg/m³)
g = acceleration due to gravity (9.81 m/s²)
h = depth of the fluid column (m)

In this case, the fluid is water and its density is approximately 1000 kg/m³. The depth of the fluid column is given as 10 m. Substituting these values into the equation, we can calculate the pressure exerted by the water:

P = (1000 kg/m³) x (9.81 m/s²) x (10 m) = 98,100 N/m² or 98.1 kPa

2. Area of the wall:
The area of the vertical wall is the height of the water level multiplied by the length of the wall. Since we are considering the force per meter length, we can assume the length of the wall to be 1 m. Therefore, the area of the wall is:

A = 10 m x 1 m = 10 m²

3. Total force:
The total force acting on the vertical wall per meter length is the product of the pressure and the area of the wall:

Total force = Pressure x Area = 98,100 N/m² x 10 m² = 981,000 N or 981 kN

Therefore, the correct option is (c) 981 kN.

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