CE 230-Engineering
Fluid Mechanics
Lecture # 22-24
MOMENTUM EQUATION
Time rate of change of a system extensive property
=
time rate of change of that property in CV
+
Net outflow rate of that property across CS
Momentum equation
Select B=linear momentum=m V
Therefore b = V



d

[mV ]   VdV   V (V . A)
dt
t cv
cs
Time rate of change of system L.M.= TROC of L.M. in C.V+Net outflow of L.M.C.S.
Special case: steady flow
the momentum equation is


 F   V (V . A)
cs
Note that these are three equation
LHS = all forces acting on fluid in c.v.
Including body, surface and external forces
Applications of ME to be examined
Forces on nozzles
Forces on bends
Forces from jets
Forces on sluice gates
Problem 6.39
Determine the components of the force needed to
hold the bend nozzle in place.
V=130 ft/s
Nozzle weight = 100lb
Problem 6.53
What if we have double nozzle?
Given V’s and sizes.
Q= 0.5m3/s
Va=Vb
Ra=5cm
Rb=6cm
Forces on bends
Example 6.7
z
x
Forces resulting from jets
Determine the force created by the steam jet on the blade.
What if the blade was moving along x with a velocity of 100m/s
Force on a sluice gate
6.3 Jet dia and v are given so is weight of tank and water
Need forces needed to hold tank
V = 20m/s
D=30mm