Fluids – Hydrostatics and Hydrostatic Pressure – MCAT Physics | MedSchoolCoach

## Hydrostatics

Hydrostatics is referring to the study of fluids at rest, as opposed to hydrodynamics, which is the study of fluids in motion. A fluid can either be a liquid or gas, and no definitive shape. In order to discuss hydrostatics, we will first define several terms relating to the characteristics of a fluid, including the density, weight, specific gravity, and pressure.

1. Density (ρ) is defined as a measure of how condensed a substance is, which we can understand through the equation mass/volume. From the equation for density, the units of density are units of mass per volume (kg/m3).

ρ=mV (kgm3)

1. Weight is synonymous with the force of gravity (Fg). In other contexts, we discuss one way of calculating weight, by multiplying an object’s mass with the gravitational constant. However, by substituting in V for mass in the equation for weight, we find that an alternative expression for weight is the density of an object times its volume. If we know the density of a fluid and we know the volume of a particular fluid, then we are able to calculate the gravitational force acting on that fluid.

Fg=mg=pVg

1. On the MCAT, specific gravity (SG) is most often defined as a measure of density relative to water. Specifically, it is calculated as the density of some substance of your choosing divided by the density of water. For the MCAT, you will need to have memorized the density of water, which can be written as 1000 kg/m3, 1 kg/L, 1 g/mL, or 1 g/cm3.  If an object is denser than the fluid it is contained in, it will sink. Therefore, we can say that if an object has a specific gravity greater than 1, it will sink. If an object has a specific gravity less than 1, it will be neutrally buoyant. If an object has a specific gravity less than 1, it will float.

SG=substancewater

1. Pressure is defined as force (N) applied over an area (m2), and therefore has units of N/m2. One N/m2 is equal to one Pascal (Pa). Various types of pressure are relevant when discussing fluids, including hydrostatic pressure and absolute pressure.

P=FA

## Hydrostatic Pressure

Hydrostatic pressure, also called gauge pressure, is the pressure that is a result of being at a certain depth within a fluid. Consider a container filled to the brim with fluid. Within the container of fluid, imagine a flat sheet of metal that has a length (l) and width (w). This is important because the sheet of metal has a particular area that is going to be acted on by the fluid, creating pressure. Pressure is equal to force/area, and when the sheet of metal is submerged in water, the force acting on the metal is the weight of the fluid above it. Recall that we defined the weight of the fluid as its density multiplied by its volume. The farther down in the container the sheet is, the greater the weight of water acting on the sheet. The pressure acting on the sheet of metal is the force of gravity over the sheet across the area of the sheet. However, we can derive an even more specific equation. The volume of water above the sheet is equal to the length of the sheet, multiplied by the width of the sheet, multiplied by the depth (h) of the sheet below the water (essentially the height of the column of water above the sheet). The length by width of the sheet is equal to area, which cancels out with area in the denominator.  The hydrostatic pressure of a fluid at a particular depth is therefore equal to the product of its density, the gravitational constant, and the depth at which it acts.

Phydrostatic=FgA=ρVgA= AghA=ρgh

## Absolute Pressure

Hydrostatic pressure does not take into account the total pressure at a particular point in a fluid. The total pressure, or absolute pressure, at a particular point, takes into account two things: the hydrostatic pressure at that point, and the atmospheric pressure. The hydrostatic pressure is the pressure due to the weight of water acting across an area, and the atmospheric pressure is the pressure due to the atmosphere pushing down on the surface of the fluid. At the very surface of a fluid, there is no hydrostatic pressure, but there is atmospheric pressure due to the air above the fluid pressing downward. If an MCAT question specifically asks you to calculate the gauge or hydrostatic pressure at a point in a fluid, you would disregard atmospheric pressure. However, it is important to remember that it exists and contributes to absolute pressure.

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