The water in a 25-m-deep reservoir is kept inside by a 150-m-wide wall whose cross section is an equilateral triangle, as shown in Fig. P10-45. Determine (a) the total force (hydrostatic + atmospheric) acting on the inner surface of the wall and its line of action and (b) the magnitude of the horizontal component of this force. Take Patm = 100 kPa.

Problem 149P

The water in a 25-m-deep reservoir is kept inside by a 150-m-wide wall whose cross section is an equilateral triangle, as shown in Fig. P10-45. Determine (a) the total force (hydrostatic + atmospheric) acting on the inner surface of the wall and its line of action and (b) the magnitude of the horizontal component of this force. Take Patm = 100 kPa.

Solution 149 P

Step 1 :

In this question, we need to find total force acting on the inner surface of the wall

In the second part, we need to find magnitude of horizontal component of total force

Data given

Depth

Width

Atmospheric pressure

Density of water

Considering the figure given

Step 2 :

We shall find the length of wall surface along the water, that is the breadth of the triangle

It is given

Hence we have obtained breadth of triangle as

Step 3 :

We shall find the resultant hydrostatic pressure of the triangle

It is given by

Therefore

Substituting values we get

Hence we have obtained resultant force as