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]
