Find the Height for Equal Pressure in a Cylinder of Water

AI Thread Summary
To determine the height of water in a cylinder where the pressure on the side walls equals the pressure on the bottom, it's essential to understand that hydrostatic pressure varies linearly with depth. The average pressure on the wall can be calculated as the arithmetic mean of the pressures at the top and bottom. The discussion concludes that the height of water should be d/2 to achieve equal pressure on the side walls and the bottom. This solution is based on the linear nature of hydrostatic pressure. The final answer confirms that d/2 is indeed the correct height.
prasanna
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Can somebody help me out in this problem?
There is a cylinder of diameter d,it is filled with water.
Upto what height should water be filled so that the pressure on the side
walls of the cylinder is equal to the pressure on the bottom?
 
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The pressure on the wall is not the same as the pressure on the bottom since it varies from top to bottom. Do you mean the total force acting on the wall due to the pressure?
 
prasanna:
Since the hydrostatic pressure is a linear function of the vertical variable, the mean value of the pressure is the arithmetic mean of the top and bottom values.
This can be used to estimate the total force on the cylindrical wall.
 
To Tide
Yes I mean the force due to pressure (sorry)
 
arildno said:
prasanna:
Since the hydrostatic pressure is a linear function of the vertical variable, the mean value of the pressure is the arithmetic mean of the top and bottom values.
This can be used to estimate the total force on the cylindrical wall.

So, When you solve I get the height is d/2.
Am I right??
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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