Question

You have made some conclusions abou the water pressure at various points in th water. Do the following to test these conclusions: a. Consider a container of water at rest. b. Imagine a cylindrical column of the water from the top of the water to a depth h below c. d. e. f. g. the top of the water assume that the cross-sectional area is A. Draw all forces acting on the column of water. You may assume that the forces on the sides on the column cancel, and thus, you can ignore them. Also, identify the source of these forces. Use Newton's 2nd law and write an equation for the vertical direction. Use the equation and derive an expression for the water pressure at the depth h. Explain how this expression agrees with Pascal's principle. Use this expression to qualitatively explain why the pressure depends on depth. What does this imply for the air?

Answer 1

If we assume a cylinder at a depth of h then there will be two force acting.

One force will be the weight of water above the column which will be acting downward.

The other force which will balance the down force is the buoyant or upper force.

Let the height of water be h. The cross section area is A.

then

F = mg

F = $\rho$Vg

F = $\rho$hAg (volume is height multiplied by area)

as we know

Pressure = force / area

Pressure =  $\rho$hAg / A

Pressure =  $\rho$hg

Pressure =  $\rho$gh

This agrees with pascal's principle as we can see that pressure increases with depth. The lowermost point in a column of liquid will have maximum pressure.