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Tuesday, 6 February 2018

TOTAL PRESSURE AND CENTRE OF PRESSURE FOR INCLINED PLANE SURFACE IMMERSED IN A LIQUID

We were discussing the basic definition and derivation of total pressure and centre of pressure in our previous posts. 

Today we will be interested to see here the expression for total pressure and centre of pressure for inclined plane surface submerged in liquid, in the subject of fluid mechanics, with the help of this post. 

Let us consider a plane surface of arbitrary shape immersed in liquid in such a way that the plane of surface makes an angle θ with the free surface of liquid as displayed here in following figure.


Let us consider that we have following data from above figure.

A = Total area of inclined surface
ħ = Height of centre of gravity of inclined area from free surface
h* = Distance of centre of pressure from free surface of the liquid
θ = Angle made by the surface of inclined plane with free surface of the liquid 

Total pressure which 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. 

Total pressure for inclined plane surface submerged in liquid will be given by following formula as mentioned here.

Total pressure = ρ g A ħ

Centre of pressure is basically defined as a single point through which or at which total pressure or total hydrostatic force will act. 

Centre of pressure for inclined plane surface submerged in liquid will be given by following formula as mentioned here.
For a vertical plane submerged surface, θ = 90 

We will find out the total hydrostatic force on curved surfacesin 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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