Determine the density of a liquid, if it exerts a pressure of $100 P a$ at a point in the depth of $1 m$ . Given the acceleration due to gravity is $10 m s^{- 2}$ .

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Solution

Step1: Given Data
$P r e s u u r e P = 100 P a, a c c e l e r a t i o n d u e t o g r a v i t y g = 10 m s^{- 2}, a n d h e i g h t h = 1 m .$
Step2: Finding Density
The pressure within the fluid arises as a result of the weight of the fluid.
In the case of static fluid, the pressure exerted at depth h is given as follows
$P r e s s u r e = d e n s i t y \times a c c e l e r a t i o n d u e t o g r a v i t y \times h e i g h t$
$P = ρ g h$
$T h u s, d e n s i t y (ρ) = \frac{P}{g h}$
$H e r e, P = 100 P a, g = 10 m s^{- 2}, a n d h = 1 m .$
$T h e r e f o r e, ρ = \frac{P}{g h} = \frac{100}{10 \times 1} = 10 K g m^{- 3} .$

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Determine the density of a liquid, if it exerts a pressure of 100Pa at a point in the depth of 1m. Given the acceleration due to gravity is 10ms-2.

Determine the density of a liquid, if it exerts a pressure of $100 P a$ at a point in the depth of $1 m$ . Given the acceleration due to gravity is $10 m s^{- 2}$ .