Fluid Mechanics Review

Fluid Mechanics

Density (p):

p= M/V

SI: kg/m^3

V=AΔX

Specific Gravity: ratio density to water at 4 degrees Celsius

pwater= 1000 kg/m^3

sp. gr. = psubstance/ pwater

Pressure (P):

P= F/A

SI: Pascals or Pa (1N/1m2)

Newton’s Third Law connection = distributing the force over a greater surface

Water Bed’s have the density of water! (Disregard other materials)

Po = atmospheric pressure, @ sea level = 101,325 Pa

1 atm = 101,325 Pa

1 atm = 14.7 lb/in2

1 atm = 760 mmHG or torr

1 torr or mmHG = 133.32 Pa

1 bar = 1,000,000 Pa

The force exerted by a fluid on an object is always perpendicular no matter which angle

Fg = mg= pVg = p(lwh)g (from density equation)

Pliquid = F/A = F(g of liquid) / A = p(lwh)g/lw = pgh

Pliquid = pgh

Static Equilibrium:

Fluid at Rest (all points at the same depth must be at the same pressure)

When an object is suspended in a liquid there is an upward force from the liquid at the bottom and a downward force that is equal and opposite from BOTH the force of gravity of the substance and the liquid on the top

Σ F = F2 – (F1 + Fg ) = 0

P2A – (P1A + mg) = 0

*M= pV=pA(Y1 – Y2)*

P2 = P1 + pgΔY

* water level = 0, meaning that

the depth below that is going to

be negative. (-Y1 – (- Y2 )) or

simply (-Y1 +Y2 )

Hydrostatic Pressure:

Ptotal = Patm+ Pliquid

Pliquid = pgh

Patm = Po

Ptotal = Po + pgh

Pguage= Ptotal – Po

Pguage = (Po + pgh) – Po

Pguage = pgh

*when there is a lid Po=0 Pa, atmospheric pressure is negligible*

Pascal’s Principle:

A change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of the container

P1 = P2

F1/ A1= F2/ A2 (F1< F2 but A1> A2)

F1= (A1/ A2)( F2)

F1/ F2= A1/ A2

Application: Hydraulic Press/Brakes ~ greater Δx over a smaller A1 from a small F1 means less Δx over a greater A2 with a larger F2

Archimedes’s Principle:

Any object completely or partially submerged in a fluid is buoyed...