Page 158 - Mechanical Engineer's Data Handbook

-- -E Symbols used:
FLUID MECHANICS 147

p =density of liquid
A=plate area
x =depth of centroid
I = second moment of area of plate about a horizontal
axis through the centroid
6 =angle of inclined plate to the horizontal
Pressure

F 11
w

Piston
area
A

Hydraulic jack

A relatively small force F, on the handle produces a Force on plate F=pgxA
pressure in a small-diameter cylinder which acts on a
large-diameter cylinder to lift a large load W: Depth of centre of pressure h=x+- I
Ax
4F 4W a
Pressure p = - -, where F = F - I sin2 6
=
nd2 nD2 ,b h=X+- (for the inclined plate)
Ax
D2 aD2
Load raised W=F-=F,--
d2 bd2

CG = centroid
CP=centre of pressure

4. I .5 Pressure on a submerged plate

The force on a submerged plate is equal to the pressure
at the depth of its centroid multiplied by its area. The
point at which the force acts is called the ‘centre of
pressure’and is at a greater depth than the centroid. A
formula is also given for an angled plate.