(I) Show that Bernoulli's equation reduces to the hydrostatic variation of pressure with depth (Eq. 1 CU3b) when there is no flow (v1 =v2 = 0).

Solution 37P:

We have to deduce hydrostatic variation of pressure with depth equation from Bernoulli’s equation.

Step 1 of 3</p>

Concept:

Hydrostatic pressure variation: The pressure difference across two point separated by the height in a liquid of density is given as,

…(1)

Step 2 of 3</p>

Figure below show the water flowing through the cube. The rate of flow of the liquid through the cube is constant.

Applying Bernoulli's equation to the cube at points (1) and (2), we get,

…(2)

Here,

Pressure at point 1 Pressure at point 2

Velocity at point 1 Velocity at point 2

Height of cube of point 1 Height of cube of point 2

Area of cube at point 1 Area of cube at point 2