Show that the pressure in liquids is given by density multiplied by gravity multiplied by height

Answer

The answer to your question is given below.

Explanation:

Pressure (P) = force (F) / Area (A)

P = F/A (1)

Recall:

1. Force (F) = mass (m) × acceleration due to gravity (g)

F = mg

2. Volume (V) = Area (A) × Height (h)

V = Ah

Divide both side by h

A = V/h

Substitute the value of F and A into equation 1.

P = F/A

P = mg ÷ V/h

P = mg × h/V

P = mgh/V (2)

Recall:

Density (d) = mass (m) /volume (V)

d = m/V

Replace m/V in equation (2) with d.

P = mgh/V

P = dgh

Where:

P is the pressure.

d is the density.

g is acceleration due to gravity.

h is height.

Pressure = Density × gravity × height

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