Assignment 7 of EP324.3 Mechanics IV 1. Air flows steadily between

Assignment 7 of EP324.3 Mechanics IV
1. Air flows steadily between two cross sections in a long, straight section of 0.1-m insidediameter pipe. The static temperature and pressure at each section are indicated in figure. If
the average air velocity at section (1) is 205 m/s, determine the average air velocity at section
(2).
Sol) Relevant principle: The continuity equation
For steady flow between sections (1) and (2),

Thus,
To determine
Then,
where
m/s and
, we use the ideal gas equation assuming air behaves as an ideal gas.
= 314 m/s
(ANSWER)
2. Determine the magnitude and direction of the x and y
components of the anchoring force required to hold in
place the HORIZONTAL 180o elbow and nozzle
combination shown in Figure.
Sol) Relevant principle: The linear momentum equation
1) x-component:
• Boundary conditions
At section (1):
,
At section (2):
,
,
(
ft/s &
,
(
&
)
: Atmosphere)
Then,


From the continuity eq.,
Then,
= −1890 lb
(To Left)
(Answer)
2) y-component:
: No y-component of V at (1) and (2), i.e.
(Answer)
3. A circular plate having a diameter of 300 mm is held
perpendicular to an axisymmetric HORIZONTAL jet
of air having a velocity of 40 m/s and a diameter of
80 mm as shown in Figure. A hole at the center of
the plate results in a discharge jet of air having a
velocity of 40 m/s and a diameter of 20 mm.
Determine the horizontal component of force
required to hold the plate stationary.
(2)
(1)
Sol) Relevant principle: The linear momentum equation
Considering the CV shown in Figure
x-component:
(
: Open to Atmosphere)
• Boundary conditions
At section (1):
,
,
(
m/s)
At section (2):
,
,
(
m/s)
Then,
(No horizontal component at upper and lower sections)
= − 9.27 N
(To Left)
(Answer)
4. A vertical jet of water leaves a nozzle at a speed of 10
m/s and a diameter of 20 mm. It suspends a plate having
a mass of 1.5 kg as indicated in Figure. What is the
vertical distance h? (Hint: Use the control volume
indicated in the figure and neglect the mass of fluid
within CV)
(2)
(1)
Sol) Relevant principle: The Bernoulli’s equation
&
The linear momentum equation
From the Bernoulli’s equation between (1) and (2)
(
: Open to atmosphere)

Using the continuity equation,

(A1, V1: Known, but A2: Unknown)
In order to determine A2, let’s use the linear momentum eq. along y-axis,
y-component:
(
)

Finally,
3.976 m
(Answer)
5. A 100-ft-wide river with a flowrate of 2400 ft3/s flows over a rock pile as shown in figure.
Determine the direction of flow and the head loss associated with the flow across the rock pile.
(Hint: Use the control volume indicated in the figure)
(1)
(2)
Sol) Relevant principle: The energy equation
To determine the direction of flow we will assume an arbitrary direction, use the energy equation,
and calculate the head loss.

Always, Head loss =
0
Therefore, if the head loss is positive, our assumed direction of flow is correct.
If the head loss is negative, our assumed direction of flow is wrong.
So, assuming the flow is from right to left or from point (1) to point (2) in the figure.
Using the energy equation,
(
: Open to atmosphere and
: No shaft work (machine))
Now
ft/s
So,
and
ft/s
= 0.32 ft (Positive)
Direction = From right to left
(ANSWER)
6. A pump is used to move water from a lake into a large, pressurized tank as shown in figure at
a rate of 1000 gal in 10 min or less. Will a pump that adds 3 hp to the water work for this
purpose? Support your answer with appropriate calculations. Repeat the problem if the tank were
pressurized to 3 atm, rather than 2 atm.
(2)
Sol) Relevant principle: The energy equation
Using the energy equation,
(1)
(a)
where
(Atmosphere),
ft,
(large reservoir),
lb/ft2
(large container)
Thus,
(1)
In addition, Volume flowrate
ft3/s using the

So that,
ft
(2)
Combining the eq. (1) with the eq. (2),
(The pump will work for
(b) If
.) (ANSWER)
lb/ft2,
Thus,
(Physically impossible)
(The pump will not work for
.)
(ANSWER)