Physics #20: Fluid Dynamics
by Qubit Factory
The mass density of a fluid (liquid or gas) is defined as
where m is the mass of the liquid and V is the volume of the liquid.
Pressure is defined as the net force per area:
Note that this can reduce to
Now, given it follows that , therefore:
Note that (thus not a vector).
Also note that the units for pressure are where the latter stands for Pascal.
Given density depth and gravitational acceleration the pressure differential between two points underwater is given by
I have realized something:
is defined in some textbooks as the weight density, but I redefine it as:
which can be seen as the net gravitational pull (acceleration) per volumetric area. Now, multiplying by h causes the following:
which can be seen as the net gravitational pull per rectilinear area. Since force is mass times acceleration, the pressure equation literally reduces into “mass times acceleration per area” in the form of gravitational pull over area.
A perturbation of pressure at one point in a fluid will diffuse to all other points within the fluid, as well as the enclosure. This is mathematically stated as:
If a fluid is flowing continuously over a surface with points of velocity, then the fluid will experience rotational motion if
The streamline for a fluid is defined as:
Fluid Mass Flow Rate:
Equation of Continuity:
Volume Flow Rate: