Consider the general form of the Reynolds transport theorem (RTT) as stated in Prob. Let B11 be the linear momentum m V → of a system of fluid particles. We know that for a system. Newton’s second law is ∑ F → = m a → = m d V → d t = d d t ( m V → ) s y s Use the RTT and Newton’s second law to derive the linear momentum equation for a control volume.
Consider the general form of the Reynolds transport theorem (RTT) as stated in Prob. Let B11 be the linear momentum m V → of a system of fluid particles. We know that for a system. Newton’s second law is ∑ F → = m a → = m d V → d t = d d t ( m V → ) s y s Use the RTT and Newton’s second law to derive the linear momentum equation for a control volume.
Solution Summary: The author explains the linear momentum equation for a control volume and the Reynolds transport theorem.
Consider the general form of the Reynolds transport theorem (RTT) as stated in Prob. Let B11 be the linear momentum
m
V
→
of a system of fluid particles. We know that for a system. Newton’s second law is
∑
F
→
=
m
a
→
=
m
d
V
→
d
t
=
d
d
t
(
m
V
→
)
s
y
s
Use the RTT and Newton’s second law to derive the linear momentum equation for a control volume.
An incompressible liquid flows along a pipe as shown. The constriction in the pipe
reduces its diameter from 4.0 cm to 2.0 cm.
Aj
A2
Where the pipe is wide, the water velocity, v1 = 8.0 m/s. The velocity of the water,
V2, at the narrow end is nearly
2.0 m/s
16 m/s
4.0 m/s
32 m/s
As we learned, Bernoulli's equation is not to be used in many situations. Let's say you are examining changes between two points in a flow.
Which ONE of these scenarios could you appropriately use Bernoulli's equation on?
O A turbine is situated between the two points
There are large changes in kinetic energy between the two points
The mass flow rate between the two points changes with time
There are large changes in density between the two points
There are large viscous losses between the two points
QUESTION 10
A 12 cm diameter jet of air strikes a plate positioned normal to the flow, with all air deflected away parallel to the plate. If the air flows at a
speed of 20 m/s, what is the force needed to held the plate in place? Do not use a linear momentum correction factor.
O 0.272 N
10.9 N
4510 N
5.45 N
0.340 N
In plane stagnation flow, an incompressible fluid occupying the space y>0 has one
velocity component given by Vx-x. The flow is two-dimensional and steady, such that
V₂=0 and nothing depends on z or time t.
(a)
Use the continuity equation to determine Vy(x,y), given that Vy(x,0) =0.
(This condition for Vy corresponds to the plane y=0 being an impenetrable boundary.)
(b)
is arbitrary, so you may set Y=0 at any convenient location.)
Determine the stream function for this flow, (x,y). (The absolute value of
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