Page 157 - Mechanical Engineer's Data Handbook

4.1 Hydrostatics

4. I. I Buoyancy
V” p”
The ‘apparent weight’ of a submerged body is less than
its weight in air or, more strictly, a vacuum. It can be
shown that it appears to weigh the same as an identical
volume having a density equal to the difference in
densities between the body and the liquid in which it is
immersed. For a partially immersed body the weight of
the displaced liquid is equal to the weight of the body. Weight of liquid displaced =Weight of body

or PLVS= PB VB
4. I .2 Archimedes principle
P
PB
‘S
Therefore: Vs = VB - or - 2
=
Submerged body PL VB PL
Let : 4. I .3 Pressure of liquids
W= weight of body
V= volume of body = W/pB The pressure in a liquid under gravity increases
pB = density of body uniformly with depth and is proportional to the depth
pL = density of liquid and density of the liquid. The pressure in a cylinder is
equal to the force on the piston divided by the area of
Apparent weight W‘= W-p,V the piston.
Then: W‘= V(pB-pp,)
The larger piston of a hydraulic jack exerts a force
greater than that applied to the small cylinder in the
ratio of the areas. An additional increase in force is due
to the handleflever ratio.

4.1.4 Pressure in liquids

Gravity pressure p = pgh
where: p =fluid density, h = depth.
Units are: newtons per square metre (Nm-’) or
pascals (Pa); lo5 N m-2 = lo5 Pa = 1 bar = lo00 milli-
Floating body bars (mbar).
F
Let : Pressure in cylinder p = -
VB = volume of body A
Vs = volume submerged where: F=force on piston, A=piston area.