Total Hydrostatic Force on Surfaces

Total Hydrostatic Force on Plane Surfaces
For horizontal plane surface submerged in liquid, or plane surface inside a gas chamber, or any plane surface under the action of uniform hydrostatic pressure, the total hydrostatic force is given by

$F = pA$


where p is the uniform pressure and A is the area.



In general, the total hydrostatic pressure on any plane surface is equal to the product of the area of the surface and the unit pressure at its center of gravity.

$F = p_{cg}A$


where pcg is the pressure at the center of gravity. For homogeneous free liquid at rest, the equation can be expressed in terms of unit weight γ of the liquid.

$F = \gamma \bar{h} A$


where   $\bar{h}$   is the depth of liquid above the centroid of the submerged area.

Problem 527 and Problem 528 | Friction

Problem 527
A homogeneous cylinder 3 m in diameter and weighing 30 kN is resting on two inclined planes as shown in Fig. P-527. If the angle of friction is 15° for all contact surfaces, compute the magnitude of the couple required to start the cylinder rotating counterclockwise.

Cylinder resting on the corner of two inclined planes


Problem 528
Instead of a couple, determine the minimum horizontal force P applied tangentially to the left at the top of the cylinder described in Prob. 527 to start the cylinder rotating counterclockwise.

Problem 522 | Friction

Problem 522
The blocks shown in Fig. P-522 are separated by a solid strut which is attached to the blocks with frictionless pins. If the coefficient of friction for all surfaces is 0.20, determine the value of horizontal force P to cause motion to impend to the right. Assume that the strut is a uniform rod weighing 300 lb.



Problem 512 | Friction

Problem 512
A homogeneous block of weight W rests upon the incline shown in Fig. P-512. If the coefficient of friction is 0.30, determine the greatest height h at which a force P parallel to the incline may be applied so that the block will slide up the incline without tipping over.

Tall block on an inclined plane


Problem 509 | Friction

Problem 509
The blocks shown in Fig. P-509 are connected by flexible, inextensible cords passing over frictionless pulleys. At A the coefficients of friction are μs = 0.30 and μk = 0.20 while at B they are μs = 0.40 and μk = 0.30. Compute the magnitude and direction of the friction force acting on each block.

Two blocks on two inclined planes connected by cords