**Variation of pressure with depth in a fluid of constant density **or *How does pressure varies with depth in a fluid of constant density?* – this is the topic of this post.

**Variation of pressure with depth in a fluid of constant density** – Lab setup

Let’s consider a fluid of constant density as shown in the Figure below. Now let’s go ahead step by step towards our objective.**Let’s take:The density of the fluid = ρThe volume of the fluid = VArea of the bottom-surface =Aand height of the fluid column = hweight of the fluid = w and mass of the fluid =m**

*How does pressure varies with depth in a fluid of constant density?* – Observations | equation of the fluid pressure

1 ) The pressure at the bottom of the container is due to the **pressure of the atmosphere (P _{0}) **plus the

**pressure due to the weight of the fluid**.

2) **The pressure due to the fluid is equal to the weight of the fluid divided by the area. **

3) Now, the

**weight of the fluid is equal to its mass times the acceleration due to gravity**

Since the density is constant, the weight can be calculated using the density:**w = mg = ρVg = ρAhg.** *[ we used these formulas above, mass = density x volume *

*=>*

&

**m**=**ρV**&

*Volume of the fluid (V)= (area of the bottom-surface) (height of the fluid*)

*=>*

]

**V = A h**]

4) Pressure due to the weight of the fluid = weight of the fluid /area = w/A =

**ρAhg**/A =

**ρhg**

5)

The pressure at the bottom of the container is therefore equal to atmospheric pressure **P _{0}** added to the Pressure due to the weight of the fluid:

**P = P**. This equation thus shows

_{0}+ ρhg*how the pressure varies with depth in a fluid of constant density*.