N-S (Incompressible) (Incompressible)
(Shear) Drag per unit width D/W:
Polar Form of N-S
Blasius
BOUNDARY LAYER:
Solutions:
̇ deficit: ,
Where
Euler: Polar form of Continuity & in x in x dirn: dirn:
∵
,
∴
&
Centre of Pressure(where F acts):
(Parallel flow: v and w=0)
,
p deficit:
Shape factor:
Slider bearing:
Boundary layer Separation
≈
Flat plate: H 2.6 (L), 1.3(T), 3(linear)
Continuity Eqn:
≈
Se arat aratio ion n: H 3.5 L 2.4 T Incompressible flow,
∆ρ=0
Drag on flat plate :
(Force=dp/dt)
,
Rayleigh Bearing , find d/dt : :
Pressure field:
Separation:
∫
Steady,2D, parallel flow: CF:
u’:Fluctuating
Bearing Pressure distribution:
&
Couette flow (top moving):
sub Into
OR:
Eqns:
̅
&
∴P
max,
Thrust/unit Width:
value
θ
since =
Von Karman:
A->the wetted area
Blasius - Non-dimensional distance
&
Eqns of Motion:
Sub in
etc, and time average each
Continuity: x Component:
̅ ( )
̅ ) ( y Component:
Turbomachinery
& since
∴
̇ ̇ ∴ & Mean Radius:
NPSH:
Forces: Geometrically similar=Homologous ,
Considering
Power
flow rate Q
Bernoulli head
SSEE:
Euler Head
Pump similarity
Power transmitted
Specific Speed:
Power to PUMP:
( ) ( ) ( ) ( ) ( ) E.g:
Static suction lift: Tendency for cavitation(pi
Head requirement:
NPSH:
Axial Pumps
and
&
Note the Centrifugal
hubs !
Geometric:
No whirl: =0,Vt1=0
Kinematic:
Pumps in //:
V1=Vn1
Pumps in series:
Torque:
=========================
&
ϕ
α
d =Vsin ds
Source+sink+uniform flow:
Doublet+Uniform flow:
,
Pressure distribution on cylinder:
Flow past rotating cylinder:
At stag pt: