If a liquid has a free surface, how can you calculate the pressure at a certain point in the liquid?

Answer Options:
Select one of the following:
A. [tex]p = hdg[/tex]
B. [tex]p = \frac{h}{dg}[/tex]
C. [tex]p = \frac{g}{hd}[/tex]
D. [tex]p = h = dg[/tex]



Answer :

To calculate the pressure at a certain point in a liquid with a free surface, you can use the hydrostatic pressure formula. Hydrostatic pressure is the pressure exerted by a fluid in equilibrium at any given point due to the force of gravity.

The formula to calculate the pressure [tex]\( p \)[/tex] at a depth [tex]\( h \)[/tex] in a liquid with density [tex]\( d \)[/tex] and gravitational acceleration [tex]\( g \)[/tex] is given by:

[tex]\[ p = hdg \][/tex]

Here’s a step-by-step explanation of the terms involved:

1. Height/Depth ([tex]\( h \)[/tex]): This is the vertical distance from the free surface of the liquid to the point where you want to measure the pressure.

2. Density ([tex]\( d \)[/tex]): This is the mass per unit volume of the liquid.

3. Gravitational acceleration ([tex]\( g \)[/tex]): This is the acceleration due to gravity, which is approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on the surface of the Earth.

Multiplying these three values together gives you the pressure at a specific depth in the liquid.

Given the answer choices:
- [tex]\( p = hdg \)[/tex]
- [tex]\( p = h / dg \)[/tex]
- [tex]\( p = g / hd \)[/tex]
- [tex]\( p = h = dg \)[/tex]

The correct option is [tex]\( p = hdg \)[/tex].

Therefore, the answer is:

[tex]\[ \boxed{p = hdg} \][/tex]