Tutorial5 .pdf


Nom original: Tutorial5.pdfTitre: Tutorial5Auteur: jmitroy

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ENG243 - TUTORIAL EXERCISES - Set 5
The tutorials for this unit will come from two sources. There are problems taken directly
from the text book. The reference MYO 03.53 would mean problem 3.53 from chapter 3
of the set textbook. The information given in the textbook is reprinted in the tutorials for
your convenience. Other problems will give full details.
Some problems are given in BG units. I recommend you convert all numbers into
SI units, and then solve the problem in SI units. You can then convert the answer back
to BG units if necessary.
1.
(MYO 04.10) The x and y components of a velocity field are given by u = x2y and
2
v = -xy . Determine the equation for the streamlines of this flow and compare it with
those in Example 4.2. Is the flow in this problem the same as that in Example 4.2?
Explain.

2.
Water flows steadily down a channel and experiences a hydraulic jump. Its
velocity in the x-direction is given by
V(x) = 1.60 m/s
V(x) = 2.00 – 0.10x
V(x) = 1.20 m/s

0.0 < x < 4.0
4.0 < x < 8.0
x > 8.0

What is the horizontal acceleration of the water in these three separate regions?
3.
(MYO 04.14) A velocity field is given by u = cx2 and v = cy2, where c is a
constant. Determine the x and y components of the accelerations. At what point (points)
in the flow field is the acceleration zero?

4.
(MYO 04.20) The velocity of the water
in the pipe shown in the figure (Fig. P4.20) is
given by V1 = 0.50t m/s and V2 = 1.0 t m/s,
where t is in seconds. Determine the local
acceleration at points (1) and (2). Is the
average convective acceleration between
these two points negative, zero, or positive?
Explain.

5.
(MYO 04.56) Water flows in the
branching pipe shown in the figure (Fig. P4.56)
with uniform velocity at each inlet and outlet.
The fixed control volume indicated coincides
with the system at time t = 20 s. Make a sketch
to indicate (a) the boundary of the system at
time t =20.2 s, (b) the fluid that left the control
volume during that time interval.

6.
(MYO 04.47) Air flows from a pipe into the region between two parallel circular
disks as shown below (Fig. P4.47). The fluid velocity in the gap between the disks is
closely approximated by

R
V = V0  
r
where R is the radius of the disk, r is the radial coordinate, and V0 is the fluid velocity at
the edge of the disk. Determine the acceleration for r = 0.5 and 2 m if V0 = 5 m/s and R
= 2 m.

7.
(MYO 04.59) Water enters a 5-fit-wide, 1-ft-deep channel as shown below (Fig
P4.59). Across the inlet the water velocity is 6 ft/s in the centre portion of the channel
and 1 ft/s in the remainder of it. Farther downstream the water flows at a uniform 2 ft/s
velocity across the entire channel. The fixed control volume ABCD coincides with the
system at time t = 0. Make a sketch to indicate (a) the system at time t = 0.5 s and (b)
the fluid that has entered and exited the control volume in that time period.

ANSWERS
1.

xy = C

2.

0 m/s2

3.

2c2x3

-0.2 + 0.01x m/s2

;

(b) 2c2y3

2

;

0.50 m/s

5.

Refer to solution

6.

800 m/s2

7.

Refer to solution.

0 m/s2

(c) x = y = 0

1.0 m/s

4.

;

12.5 m/s2

2

;

Positive – since

u

∂u
>0
∂x


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