# Fluid Mechanics

A circular disc having a diameter of 125cm is immersed in water so that the distance of its perimeter measured vertically below the water surface varies between 60cm and 150cm. Find the total force due to the water acting on one side of the lamina, and the vertical distance of the centre of pressure below the surface.

Can someone please show me how to solve this problem?

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1. The pressure at a depth of x is p(x)=ρgx.
The total force acting on any immersed surface can be calculated by integrating over the depth, i.e. x=h1 to h2.
h1 and h2 in this particular case is 60 and 150 cm respectively.

To find the centre of pressure, integrate x*p(x) over h1 to h2, and divide by the total pressure obtained above.

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2. can show the step ? pls

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3. do you have any idea from where this quesiton was taken please? Like a book ?

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4. center of mass = ((150-60)/2)+60 = 1.05
area = (1/4)*pi*D^2 = 1.227
Force = density*g*area*centerOfMass
Force = 1*9.81*1.227*1.05
Force = 12.639KN

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