Tutorial1 .pdf


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ENG243 - TUTORIAL EXERCISES - Set 1
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 01.12) A formula for estimating the volume rate of flow, Q, over the
spillway of a dam is


V2 

Q = B × C 2 g  H +
2 g 


3/ 2

where C is a dimensionless constant, g is the acceleration of gravity, B is the spillway
width, H is the depth of water passing over the spillway, and V is the velocity of water
just upstream of the dam. Is this equation dimensionally correct?

2.
(MYO 01.14) Express the following quantities in SI units: (a) 10.2 in./min, (b)
2
2
4.81 slugs, (c) 3.02 lb, (d) 73.1 ft/s , (e) 0.0234 lb⋅s/ft .

3.
(MYO 01. 23) An important dimensionless parameter in certain types of fluid flow
problems is the Froude number defined as

Fr =

V
gl

where V is a velocity, g the acceleration of gravity, and l a length. Determine the value
of the Froude number in SI units for: V = 10ft/s, g = 32.2 ft/s2, and l = 2 ft (convert these
numbers to SI before calculating the Froude number). Recalculate the Froude number
using the original BG units. Explain your answer in both SI and BG units.
4.
(MYO 01.32) The density of nitrogen contained in a tank is 1.5 kg/m3 when the
temperature is 25 °C. Determine the gauge pressure of the gas if the atmospheric
pressure is 97 kPa.
5.
(MYO 01.36) A tyre having a volume of 2.50 ft3 contains air at a gauge pressure
of 30 psi and a temperature of 70 °F. Determine the density of the air, the mass, and
the weight of the air contained in the tyre.

6.
(MYO 01.44) The viscosity of a certain fluid is 5×10-4 poise. Determine its
viscosity in both SI and BG units.

7.
(MYO 01.56)The sled shown below (Fig P1.56) slides along on a thin horizontal
layer of water between the ice and the runners. The horizontal force that the water puts
on the runners is equal to 5.0 N when the sled’s speed is 15 m/s. The total area of both
runners in contact with the water is 75 cm2, and the viscosity of the water is 1.5×10-3
N⋅s/m2. Determine the thickness of the water layer under the runners. Assume a linear
velocity distribution in the water layer.

8.
(MYO 01.58) A Newtonian fluid having a specific gravity of 0.92 and a kinematic
viscosity of 4.5×10-4 m2/s flows past a fixed surface. Due to the no-slip condition, the
velocity profile near the surface is shown below (Fig P1.58). Determine the function
du
representation of the velocity gradient (i.e.
). From this, determine the magnitude
dy
and direction of the shearing stress developed on the plate. Express your answer in
terms of U and δ , with U and δ expressed in units of metres per second and metres,
respectively.

ANSWERS
1.

Yes

2.

(a) 4.32 mm/s

3.

1.25 ; 1.25

4.

36.0 kPa

5.

3.65 kg/m

6.

5×10 Nsm

7.

3.38 ×10-5 m

8.

-2
0.621 U/δ Nm acting to left on plate

-5

3

(b) 70.2 kg

2.28 lbm/ft

3

(c) 13.4 N

(b) 0.258 kg

-2

(d) 22.3 ms-2

(d) 2.53 N

-2

(e) 1.12 Nsm .


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