Density = mass per unit volume. ρ = m/V
Pressure = Force per unit area. P=F/A
Pressure is a scalar quantity; it has no direction of its own. Pressure always creates a force at right angles to any surface exposed to the pressure.
The pressure P at a depth d in a fluid of density ρ whose surface is at a pressure P0 is given by Pascal's principle as
P = P0 + ρgd.
An object of volume V entirely surrounded by a fluid of density ρ feels an upward, Bouyant, force FB=ρVg.
REMEMBER that that is the density of the surrounding fluid not the densityof the object!!!
When fluids move they are always subject to the condition that their mass is conserved.
In addition, for steady, non-turbulent flows, energy conservation leads to Bernoulli's equation which states that the quantity
P + ½ρv2 + ρgh
is conserved.