Given:
- Base of the isosceles triangular plate = 3 m
- Altitude of the isosceles triangular plate = 3 m
- Specific gravity of oil = 0.8

To find: Distance of the center of pressure from the free surface of oil

Concepts used:
- Center of pressure
- Moment of fluid force
- Hydrostatic pressure

Solution:
1. We can assume that the isosceles triangular plate is divided into two right triangles with base and height both equal to 3/2 m.
2. Let's consider the left triangle and find the horizontal distance from the centroid of the triangle to the vertical line passing through the centroid of the triangle.

- Centroid of the left triangle will be at a height of 2/3 times the altitude from the base of the triangle.
- Therefore, h = 2/3 × (3/2) = 1 m (height of centroid from the base).
- The horizontal distance from the centroid to the vertical line passing through the centroid will be half the base of the triangle.
- Therefore, b/2 = 3/4 m (base of triangle divided by 2).
- Using Pythagoras theorem, the horizontal distance d can be found as follows:
d² = (3/4)² + 1²
d² = 9/16 + 1
d² = 25/16
d = 5/4 m

3. Now, let's find the vertical location of the center of pressure.
- The hydrostatic pressure at any depth is given by P = γh, where γ is the specific weight (weight per unit volume) of the fluid and h is the depth.
- The pressure distribution on the left triangle will be triangular, with the pressure at the base being zero and increasing linearly with depth.
- The average pressure on the left triangle can be found as follows:
Average pressure = (P1 + P2 + P3)/3, where P1, P2, and P3 are the pressures at one-third depth, two-third depth, and full depth, respectively.
- P3 = γh = 0.8 × 3 = 2.4 kN/m²
- P1 = γh/3 = 0.8 × 1 = 0.8 kN/m²
- P2 = γh × 2/3 = 0.8 × 2 = 1.6 kN/m²
- Average pressure = (0.8 + 1.6 + 2.4)/3 = 1.6 kN/m²

4. The moment of fluid force about any point is given by the product of the force and the perpendicular distance from the point to the line of action of the force.
- Let's consider the left triangle and find the moment of fluid force about the vertical line passing through the centroid of the triangle.
- The force on the left triangle can be found by integrating the pressure distribution over the area of the triangle.
- Force = ∫PdA = ∫(0.8h)bdh, where h varies from 0 to 3/2 m and b is the base of the triangle (3/2 m).
- Force = 0.8b∫h^2dh = 0.8 × (3/

Brian and Faith are students from Kenya Water Institute. After spending sometime carrying out a research, they discovered that there was need to analyze the hydrostatics law. Outline how they can determine; i. The pressure at a depth of 15m below the free surface of water in a reservoir. (2 marks) ii. Determine the height of water column corresponding to a pressure of 54KN/m2