We were discussing the
basic definition and significance of Pascal’s
Law along with its derivation , Vapour
pressure and cavitation, Absolute
pressure, Gauge pressure, Atmospheric pressure and Vacuum pressure, pressure
measurement, Piezometer, Single
column manometer and also the basic concept of U-tube
manometer in our previous posts.
Today we will understand
here the basic concept of total pressure, in the subject of fluid mechanics,
with the help of this post.
Total pressure
Total pressure is also
termed as hydrostatic force. Total pressure is basically defined as the
hydrostatic force applied by a static fluid on a plane or curved surface when
fluid will come in contact with the surfaces. This hydrostatic force will act
normal to the surface.
Let us consider that we
have one tank filled with liquid e.g. water. Let us consider that there is one
object of arbitrary shape immersed inside the water as displayed here in
following figure.
Now there will be one
hydrostatic force exerted over the object due to the weight of fluid kept
inside the tank and this hydrostatic force will be considered as total
pressure.
Total pressure or
hydrostatic force will be determined by the following formula as mentioned
here.
Total Pressure =
Derivation of total pressure
In order to determine the
total pressure, we will consider the object in terms of small strips as displayed
here in following figure. We will determine the force acting on small strip and
then we will integrate the forces on small strips for calculating the total
pressure or hydrostatic force on object.
Let us consider the small
strip of thickness dh, width b and at a depth of h from free surface of liquid
as displayed here in above figure.
Intensity of pressure on
small strip, dp = ρgh
Area of strip, dA = b x dh
Total pressure force on
small strip, dF = dP x dA
Total pressure force on
small strip, dF = ρgh x b x dh
Total pressure force on
whole surface, F = Integration of dF
Where,
ρ = Density of liquid (Kg/m3)
g = Acceleration due to
gravity (m/s2)
A = Area of surface (m2)
ħ = Height of C.G from free surface of liquid
(m)
Unit of total pressure
As total pressure is basically
a hydrostatic force and therefore total pressure will be measured in terms of N
or KN.
We will discuss Centre of pressure, in the subject of fluid mechanics, in our next post.
Do you have any
suggestions? Please write in comment box.
Reference:
Fluid mechanics, By R.
K. Bansal
Image Courtesy: Google
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