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Lets say that i have 2 different types of containers, one cuboidal and another one conical. and lets say both these are massless and fully contain water.

**1.**In the cuboidal one the pressure exerted by liquid column at base is Densitygheight.This multiplied by Area of base will give the force exerted on base.As the container is massless total downwards force is also same.And now by calculating volume and density of liquid , we can find mass of liquid and multiplying by 'g' gives total downwards force.In this case total downward force calculated by both the methods is equal.

**2.**In the conical container, the total downwards force calculated using densitygheight and multiplying by conical container's base area is 3 times greater than the force calculated using volume and density relationship(As the volume is 1/3*height*area).Why is it different, which method is correct to calculate downward force? Why is it so?


marked as duplicate by John Rennie, Kyle Kanos, Gert, user36790, JamalS Nov 28 '15 at 13:39

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  • $\begingroup$ The pressure (Pascal's Law) is given by the weight of the column of water above the measuring point: $p=\rho gh$. The shape of the container doesn't enter into it although the shape can limit the maximum depth of the measuring point. $\endgroup$ – Gert Nov 26 '15 at 17:28
  • $\begingroup$ Not exactly but yeah partly same, because i also want to know which is right method to calculate total downward force? $\endgroup$ – Shahbaaz1104 Nov 27 '15 at 15:14

In the conical container, the downforce is certainly the same. It can be found via calculus, taking into account the following:

  • Since the inside surface of the container is touching the fluid, the calculation is a surface integral.
  • The force on a surface due to a pressure is exerted perpendicular to the surface. The downward component will have to include a $\cos(\theta)$ term. For an upright cone standing on its tip, this will be a constant factor.
  • The pressure depends on the depth of water above the point being considered.

Even though the area of the tilted part of the cone is much larger than the bottom of the cube, the total downward force will still be the same.

  • $\begingroup$ Which is right method to calculate the total downwards force then? So if base is resting on the table , will the water inside the container exert outward force, so as i said ρgh gives 3 times greater result than by calculating weight of water and finding the force, so is it the outward force that needs to be subtracted? $\endgroup$ – Shahbaaz1104 Nov 27 '15 at 15:17
  • $\begingroup$ If the base is resting on the table, the outward force on the sides of the container is partly upwards, must be calculated using the calculus method, and will reduce the net downward force on the base. $\endgroup$ – Spirko Nov 27 '15 at 15:26

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