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The water in a 25 m deep reservoir is kept inside by a 150 m wide wall whose cross section is an equilateral triangle. Determine a) the total hydrostatic force acting on the inner surface of the wall and its line of action, b) the magnitude of the horizontal component of this force.

Question-AnswerCategory: Fluid MechanicsThe water in a 25 m deep reservoir is kept inside by a 150 m wide wall whose cross section is an equilateral triangle. Determine a) the total hydrostatic force acting on the inner surface of the wall and its line of action, b) the magnitude of the horizontal component of this force.
Mazurek Gravity Staff asked 4 months ago

The water in a 25 m deep reservoir is kept inside by a 150 m wide wall whose cross section is an equilateral triangle. Determine a) the total hydrostatic force acting on the inner surface of the wall and its line of action, b) the magnitude of the horizontal component of this force.

1 Answers
Mazurek Gravity Staff answered 4 months ago

Step 1:
Consider hc as the hydrostatic center of the water, b is the length of the side at which the hydrostatic force, FR is the hydrostatic force, yb is the distance of the point of action of resultant force along the wall of reservoir and h is the height of water level. Draw the figure indicating all the forces acting on the reservoir as follows:
Mechanical Engineering homework question answer, step 1, image 1

 

Step 2

Write the trigonometric identity of sine  Î”ABC.
Mechanical Engineering homework question answer, step 2, image 1
Write the trigonometric identity of sine for ΔADE.
Mechanical Engineering homework question answer, step 2, image 2

 

Step 3

Write the expression of the resultant hydrostatic force.
Mechanical Engineering homework question answer, step 3, image 1

 

Step 4

Understand that the reservoir is not fully submerged in water. Thus, s = 0. Write the expression of the distance of the point of action of resultant force along the wall of the reservoir.
Mechanical Engineering homework question answer, step 4, image 1

 

Step 5 (b)

Consider FH as the horizontal force component of the hydrostatic force. Write the expression of the horizontal component of hydrostatic force.
Mechanical Engineering homework question answer, step 5, image 1

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