Fluid Pressure (Definition)
We define the fluid pressure
P to be equal to the weight density
the depth of the fluid h.
The pressure is equal in all directions
Force on a Submerged Rectangular Sheet
P = wh = (62.4)(5) = 312
The total force on the plate is
PA = (312)(6) = 1872
Force on a Vertical Surface
DF = 62.4(4 + y)(D A) = 62.4(4 + y)(3)(Dy)
Hence the total force is
= 1123.2 pounds
A radius 2 feet circular portal is vertically submerged so that its center is 20 feet below the surface of the water. Find the total force of the water on the portal.
We write s in terms of z by the Pythagorean theorem:
depth at this cross-section is
recognize the first integral as the area of the semi-circle of radius 2.
For the second integral, let
In the VIP suite, the glass window is in the shape of an equilateral triangle with diagonal length 2 such that the top of the triangle is submerged 5 feet below the water. What total force will this window be subjected to?