8/9/2019 Fluids Dynamics Formula Sheet

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=   3 

     = 

−   =∆∆ 

--------------------------------------------------------

 

=∀

=  

3

 

→ =× −  → = ×  

----------------------------------------------------------                 4° 

=  ° =

.×  

----------------------------------------------------------

Pressure vs depth (incompressible fluids) 

    = .     = .     = = . .   = = . .. 

  =  =

. ..      

∴   =  

Pressure vs depth (compressible fluids)  + ∆  − − ∆ = 0 

( + ∆)−−∆ = 0 

∴   ∆ = ∆ 

----------------------------------------------------------

r pressure of fluid in container with lid open.

Assume fluid is incompressible. 2 =   =   = 1.01325 × 105 ∆ = ∆  1 − 2 =  

∴   = +  

----------------------------------------------------------  &   = +  ----------------------------------------------------------

 

 

 

 

 

 

     . 

≡    = − ∆∀ ∀ = − ∆∆∀ ∀  

----------------------------------------------------------    −            =

       

 Δ    Δ = Δ   =    = Δ  Δ Δ =

Δ Δ  

=

= 

 

Temperature has a srong effect on viscosity

May depend on the rate of shear strain

Assumptions often used in fluid mechanics-*viscosity is constant (Newtonian fluid)

*viscosity is 0 (ideal fluid, inviscid fluid, flow is frictionless)

--------------------------------------------------------------    =  

--------------------------------------------------------------  

Pascals principle

‘if an external pressure is applied to a confined fluid,

the pressure at every point within the fluid increases

by that amount’  

eg Hydraulic Lift 1 = 2 1 1 =

2 2  

Can be used to obtain mechanical advantage

2 = 1

 2

 1

 

Work done is the same by which the surface A2 risesis smaller than the change in the height of surface

with area A =  

--------------------------------------------------------------

Buoyancy  

Pressure increases with depth. So the pressure at 

the bottom of a floating object is greater than on

top. Thus the water exerts a net upward force on

the object. This is the boyant force.     >      

 Archimedes’ Principal 

The boyant force on an object immersed in fluid isequal to the weight of fluid displaced by that object. = ′ = ′ 

Pressure on the top surface1 =  

Force on the top surface1 = 1  = 2 

Pressure on the bottom surface2 = 2 

Force on then bottom surface2 = 2  = 2  

F B is the net force exerted by the fluid on the

submerged object  = 2 −1 = 2 − 1 = Δ 

=   =  

--------------------------------------------------------------  (conservation of mass)  1 = 2    =    =   

() − () = 0 

For multiple inputs & outputs

  =    

--------------------------------------------------------------

  

(conservation of energy)

1 +1

211

2 + 1 = 2 +1

22

2 + 2 

Further common assumptions ONLY FOR SV

1 +

2 =

 

 

1 = 0 

--------------------------------------------------------------  

Ideal Gas equation

=   =  

=   = 8.3145 −1−1 

--------------------------------------------------------------

Real Gas equation

=

 

 Z= compressibility & is dimensionless

--------------------------------------------------------------

Root-mean-square atomic velocity 

=      

T= Temperature Kelvins

m= mass

M= Molar mass of gas

-------------------------------------------------------------STP 

P=101.325 kPa T=273.15K 22.414L

--------------------------------------------------------------

Mark Riley

markriley1985@hotmail.com

8/9/2019 Fluids Dynamics Formula Sheet

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