Fluid Depth, Density, Gravity, and Pressure Calculator P = ρ·g·h

Calculate Fluid Depth & Pressure Parameters
Select Answer Mode
Depth (h) [?]

Density (ρ) [?]

Gravity (g) [?]

Surface Pressure (P_surface) [?]

Fluid Pressure (P_fluid) [?]

Total Pressure (P_total) [?]

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Contents

User Guide

This tool will calculate any of parameters defined by the hydrostatic pressure formula P = ρ·g·h which includes depth, density, gravity and pressure.

Hydrostatic pressure measurement is a common method for determining fluid depth without using floats, long physical probes or measuring tapes. Assuming a constant density and acceleration due to gravity, depth is linearly proportional to the fluid head pressure.

The measurement of hydrostatic pressure is often made using a device which reads the pressure relative to the surface pressure, since this eliminates the need to account for surface pressure which is cancelled out. However this is not always practical in applications such a submarines or sealed pressurised tanks. In these cases it is necessary to measure the surface pressure so that it can be subtracted from the overall total pressure to determine the fluid pressure component to convert into a depth reading.

Formulas

The formulas used by this fluid depth, density, gravity and pressure calculator to determine each of the individual parameters are as follows:

h = (P_total – P_surface) / (ρ · g)

ρ = (P_total – P_surface) / (g · h)

g = (P_total – P_surface) / (ρ · h)

P_surface = P_total – (ρ · g · h)

P_fluid = ρ · g · h

P_total = P_surface + (ρ · g · h)

Symbols

h = Fluid depth
ρ = Density of fluid
g = Acceleration due to gravity
P_surface = Pressure above the fluid surface
P_fluid = Hydrostatic pressure contribution form the head of fluid
P_total = Combined pressure due to fluid and surface pressure

Depth (h)

This is the vertical distance from the surface of the fluid to the point where the pressure is measured.

Density (ρ)

This is the amount of mass per unit volume of the fluid being measured. The variation in density of different fluids is a significant factor in converting hydrostatic pressure to depth. For example if the difference in density of one fluid is 2x that of another fluid, then the difference in hydrostatic pressure will also be 2x.

In addition to manually entering fluid density, you can also select a number of preset fluid densities for freshwater (1000 kg/m³), seawater (1025 kg/m³, diesel (850 kg/m³) and petrol (750 kg/m³). All of these figures reflect common values which are used as average examples, since density will vary with temperature and slight variations in the chemical composition of the fluid.

Gravity (g)

This the acceleration due to gravity acting on the fluid. Gravity is the acting force on the fluid which produces the hydrostatic pressure.

Since the level of gravity varies by only a very small percentage at sea level, the standard value of 9.80665 m/s² (g₀) is typically used, rather than adjusting to a more precise local gravity value. A button is provided for the quickly selecting ‘g₀’.

Surface Pressure (P_surface)

This is the pressure measured at the fluid surface.

If the fluid is open to the air or contained within a vented tank then the surface pressure will be atmospheric pressure.

The surface pressure is important to consider because it is pressing on the fluid and adds to the pressure measured within the fluid.

Fluid Pressure (P_fluid)

This is the pressure measured in the fluid due to gravity acting on the fluid at a particular level, and excludes any additional pressure acting on the surface of the fluid.

In many hydrostatic pressure measurement applications, the pressure is measured relative to atmospheric pressure, which eliminates the need to measure the surface pressure, providing a reading of fluid head pressure only, which is directly proportional to the depth.

Total Pressure (P_total)

This is the combination of the pressure due to gravity acting on the fluid, and the pressure at the surface.

It is not always possible to remove the surface pressure from the depth measurement calculation due to the constraints of the installation or application.

For example, in a sealed tank it may not be possible to measure the fluid pressure relative to the surface pressure, and therefore the total pressure is measured instead which includes the surface pressure, and a separate measurement device has to be used to measure the surface pressure.

Another example would be measuring the depth of a submarine where the total pressure is measured externally, and the barometric pressure has to be communicated separately from the surface, so that the true depth can be determined.