A circular plane lamina is immersed inclined in water such that the distance of its parimeter measured vertically below the water surface varies between 0.6m and 1,5m. Find the total hydrostatic force acting on the side of the lamina, and the vertical distance to the depth of pressure

To find the total hydrostatic force acting on the side of the circular plane lamina, we need to integrate the pressure acting on each part of the lamina.

First, let's calculate the pressure at a specific depth. The hydrostatic pressure at any depth in a fluid is given by the equation:

P = ρgh,

where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.

Since we are dealing with water, the density ρ is approximately 1000 kg/m³, and the acceleration due to gravity g is approximately 9.8 m/s².

Now, let's divide the circular lamina into small vertical strips. Each strip will have its own depth and width. We can consider the width of each strip as infinitesimally small, and assume that the pressure acting on it is constant. Thus, we can calculate the pressure acting on a particular strip by taking the average of the pressures at the two depths on either side.

Let's denote the depth of the lower part of the strip as h1 and the depth of the upper part as h2. The width of the strip can be represented as Δw, where Δ denotes a small change.

The average pressure acting on each strip can be calculated using the formula:

P_avg = (P(h1) + P(h2)) / 2

To find the total hydrostatic force, we need to integrate the average pressure over the entire perimeter of the lamina. Since the lamina is a circle, we can express the perimeter length at any particular depth as 2πr, where r is the radius of the lamina.

The expression for the total hydrostatic force (F) can be written as:

F = ∫[P_avg(h) * 2πr] dh

To find the vertical distance to the depth of pressure, we need to calculate the centroid of the submerged area. The centroid of the circular lamina will be at a distance of h_c below the water surface, where h_c represents the vertical distance to the centroid.

The vertical distance from the centroid to the depth of pressure can be calculated by finding the difference between the distance of the centroid below the water surface (h_c) and the average depth of the submerged lamina (∆h_avg).

The expressions for the total hydrostatic force (F) and the vertical distance to the depth of pressure can be determined by calculating the integrals and solving the equations. However, since the specific dimensions of the circular plane lamina are not provided in the question, an exact answer cannot be given without additional information.