Fluid mechanics notes

, -


Week 1 -




LECTURE 1 LECTURE 2

Three fundamental concepts like with solid mechanics : , Viscosity : This is the term for almost a value defining the
F = ma internal friction which allows a liquid to resist

Conservation of Energy Shear forces.

Conservation of Momentum

Inviscid Fluid : Theoretical liquid with Zero
viscosity meaning ,




However F = ma appears
slightly differently : it would not move at all with shear force


Pressure Viscous forces External

& - ↑
p( u) m2u m)2u) F + u .
= -


p + + + High viscosity : High friction ,
small deformation. E .

g Treacle
.
----
mass Acceleration orce
Low
viscosity : Low friction , high deformation . E .

. Water
g


This is the Navier-Stokes equation ,
and
you don't solve it Calculations
outright . You have to make
simplifying assumptions. Force F n + bu




.
, >
Sx
-



How To Define Fluids
i by " ↳
Fluids and solids both respond the same to normal


forces as : Force We therefore can calculate :
,
Pressure =
Area


But fluids

forces
and solids respond

forces applied
differently to
the side of a substance.
shear So-subt tanda = ba
=
so
along
S&Velocity gradient
,




Solids
may deform slightly ,
but will resist eventually . =
Just in the fluid
Fluids will continue to deform and won't resist
.


This tells us that the velocity gradient is dependent on


Fluid A : substance which cannot remain at rest
viscosity and shear stress F
T =A
When acted on by a shear force.

Newtonian Fluids : Fluids whos viscosity is constant with

Fluid Continuum respect to shear force .




bu
T =



Solid
Mby
mechanics single bodies interacting [
addresses High M
.
Shear
thinning
Fluid mechanics involves lots of molecules ,
so we focus M= viscosity
the of these forces. The fluid continuumided Shear
thickering
on
average

suggests that
steady state fluids can be addressed by Dynamic viscosity :
M Low M


looking at the average of the overall fluid
,
despite the Pas Nsm2 ,
, Kgm's
fact that some parts may be
behaving differently . E
.
g
Se
.




M
Fluid
going into a funnel of area and out of a Kinematic viscosity V
gradient
larger
: = =

& M

smaller area will be
moving faster at the exit than mas" , Nmskg
entrance, but the fluid may still be considered to be
V
If d is small can assume
you
moving without acceleration as long as fluid cont
3

the ,

&


a linear relationship :
inves to enter and leave at the same rate. d



y



Stationary
T =

MOU Su
This is the case for most circumstances.

, Example

A linear bearing is made of two plates separated by a film

of grease which behaves as a Newtonian fluid with dynamic
viscosity 0 .
65 kg/ms. The upper plate moves at V = 1 Om/S
.




While the lower plate is stationary distance between
. The
the plates is 0 2 mm and the plate dimensions are
. 100mm X
,




10mm . Calculate the force required to move the plate



V = 1
= 2103 0 .
= 5000

M = 0 65 .




d= 0 2 . T =

Mb =
0 65.
.
5000 = 3250Pa




F = TA =
3250 .
(0 .
1 .
0 . 01) = 3 25N.




Spinning Plate
Assuming small gap :




i
&Mur
T, w
Su wr
- T =

Spinning Plate by n

Y4r ↑ n
T = Fr =
CAr all with r
Stationary Plate vary
j f
R




SA T(r+ br)2 Tra
i
= -




-
A SA = Tr2 + 2Trbr +br2-Thr2
jA
R SAF2TLrbr
L




T = Fr = ATr ST = Mwr2trbr .
r




T= grm trad T =
2Mw gas
T= 2TMWr 2 MFTWRa
2nT