Fluid Dynamics Flashcards
ideal fluid
- steady flow
- incompressible and homogenous
- 1-D velocity profile
velocity head
U^2 / 2g
pressure head
P / ρ g
Hydraulic grade
= pressure head + elevation
= P / ρg + z
Total Energy
= Hydraulic grade + velocity head
= P / ρg + z + U^2 / 2g
stagnation point
point of no flow
reservoir assumptions
fluid velocity inside a reservoir = 0
free jet assumptions
pressure within a free jet of water = 0
Energy at any point on flow cross section is the same provided:
- the flow velocity profile can be approximated as uniform
2. The only forces acting on the fluid are weight and pressure (hydrostatic pressure distribution)
Two main types of energy loss in pipes
h(f) = friction loss h(m) = local losses (valves, constrictions)
friction loss
h(f) = fL/D * V^2/2g
f
friction factor - describing friction resistance of pipe
Re
Reynolds number = VD / ѵ
- Re
low Re
hydraulically SMOOTH
- roughness height has no effect
mid-range Re
Transition
- f varies with Re and roughness
high Re
hydraulically ROUGH (loose cell viscous sublayer) - depends only on roughness
f (Laminar flow)
f = 64 / Re
f (turbulent flow)
Swarmee and Jain Equation
f = 1.325 /
h(m)
local/minor losses
h(m) = k V^2 / 2g
k (entry into pipe from reservoir - square entrance)
0.5
k (exit into reservoir)
1.0
Gate Valve
- low head loss
- plate lifted away (small energy effect)
Butterfly Valve
- for shedding head
- plate rotated
Problems with Negative Pressure
- Blockage (0
System Curve
= Total Energy (B) - Total Energy (A) + h(f) + h(m)
Pump efficiency
e = Power (out) / Power (in) e = ɣQh(p) / Power (in)
Pump Selection Procedure
- Find pump that intersects system curve at flow that client is happy with
- Ensure pump is working at high efficiency
- Ensure pump will not cavitate
NPSH
net positive suction head
- NPSHA upstream of pump > NPSHR
Pump Groups Steps
- work out total Q and total h(p) relationships
- combine all pumps into single pump curve
- solve system like it is single pump using combined pump curve
Pumps in Series
Qtot = Q1 = Q2
h(p) tot = h(p,1) + h(p,2)
Pumps in Parallel
Qtot = Q1 + Q2
h(p) tot = h(p,1) = h(p,2)
