L-3/T-1/ME Date: 18/09/2021
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, BUET
L-3/T-1 B.Sc. Engineering Examinations 2019-2020
Sub: ME 321 (Fluid Mechanics I)
Full Marks: 210 Time: 2 Hours 30 minutes
The figures in the margin indicate full marks.
Symbols used have their usual meaning and interpretation.
ASSUME REASONABLE VALUES IF DATA ARE MISSING
USE SEPARATE SCRIPTS FOR EACH SECTION
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SECTION-A
There are FOUR questions in this section. Answer any THREE
1. (a) Gate AB in the following figure is a homogeneous mass of W kg, 2.5 m wide into the paper, (16)
hinged at A, and resting on a smooth bottom at B. For what water depth h will the force at point
B be zero? Use the following data:
Specific gravity of Glycerin = 1.263
Weight of the gate, W = (Last two digits of your student ID + 150) kg
Depth of Glycerin, H = (0.003*Last three digits of your student ID + 2) m
Fig. for Q. No. 1(a)
(b) Curved panel BC in the following figure is a 60 deg arc, perpendicular to the bottom at C. If the (19)
panel is D m wide into the paper, estimate the resultant hydrostatic force of the water on the
panel. Take,
D = (0.003*Last three digits of your student ID + 4.5) m
R = (0.003*Last three digits of your student ID + 2.5) m
Fig. for Q. No. 1(b)
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2. (a) A tank of water H m deep receives a constant upward acceleration az. Determine (i) the gage (15)
2
pressure at the tank bottom if az = 5 m /s and (ii) the value of az that causes the gage pressure
at the tank bottom to be 1 atm. Assume no spilling of water.
Take, H = (4 + 0.01*Last two digits of your student ID) m
(b) The 45 deg V-tube in the following figure contains water and is open at A and closed at C. What (20)
uniform rotation rate in rpm about axis AB will cause the pressure to be equal at points B and
C? For this condition, at what point in leg BC will the pressure be a minimum?
Take, H = (35 + Last digit of your student ID) cm
H cm
Fig. for Q. No. 2(b)
3. (a) An L cm long cylinder has a cross section of 25 cm x 25 cm. It is composed of material with (16)
specific weight 8000 N/m3. Will it float in water with its square ends horizontal?
Take, L = (35 + Last digit of your student ID) cm
(b) Consider two sources having equal strengths located along the x- axis at x = 0 and x = 2 m, and (19)
a sink located on the y- axis at y = (2 + Y) m. Take, Y = 0.1*Last digit of your student ID.
Determine the magnitude and direction of the fluid velocity at x = 4 m and y = 0 due to this
combination if the flow rate from each of the sources is 0.5 m3/s per m and the flow rate into the
sink is 1.0 m3/s per m.
4. (a) A stream function is given as follows- (20)
(i) Is it a possible (valid) stream function for a potential flow?
(ii) If so, find the velocity potential.
(iii) Locate the stagnation points, if there is any.
(iv) Assuming water to be flowing, find the pressure along the x-axis if p = 50 kPa at x = ∞.
(b) The bottom of a river has a 4 m high bump that approximates a Rankine half-body as shown in (15)
the following figure. The pressure at point B is 130 kPa, and the river velocity is 2.5 m/s. Use the
theory of inviscid flow to estimate the water pressure at point A on the bump, which is 2m above
the point B.
Fig. for Q. No. 4(b)
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SECTION-B
There are FOUR questions in this section. Answer any THREE
5. (a) An object with characteristic length of 0.2 m is flying at a speed of 1500 m/s. Consider two (15)
situations when the object is flying at two different altitudes of 10 km (Altitude - A) and 100 km
(Altitude - B) from the average sea-level height. The thermodynamic and other properties of air
at these altitudes are given below:
Altitude - A Altitude - B
Parameter 10 km 100 km
(from sea-level) (from sea-level)
Pressure (Pa) 28500 0.032
Temperature (K) 220 195
Viscosity (Pa.s) 1.8×10−5 1.8×10−5
Mean free path (m) 1.96×10−7 1.42×10−1
(i) Determine the Reynolds number of flow at Altitude - A and Altitude - B. Are the flows laminar
or turbulent at these altitudes?
(ii) Is the ‘continuum hypothesis’ valid for flow analysis in both the altitudes? Justify your
comment.
(b) Briefly explain the concept of material derivative. A velocity field and density field in Cartesian (10)
space is given as:
L
V iˆ (m/s)
t
Kte x / L (kg/m3 )
where L and K are constants. Find the material derivative of the density, ρ.
(c) Suggest a suitable equipment for measurement of free-stream air velocity in a wind tunnel. Also (10)
explain the working principle of such equipment with necessary schematic diagram(s).
6. (a) With necessary diagram (s), briefly explain the static, stagnation and dynamic pressures in the (10)
context of fluid dynamics?
(b) Determine the volumetric flow and the pressure in the pipe at A if the height of the water column (10)
in the Pitot tube is 0.3 m and the height in the piezometer is 0.1 m as shown in Fig. for Q. 6(b):
Fig. for Q. No. 6(b)
(c) A fireboat draws seawater (SG = 1.025) from a submerged pipe and discharges it through a (15)
nozzle, as in Fig. for Q. 6(c). The total head loss is 20 kPa. If the pump efficiency is 65 percent,
what horsepower (HP) motor is required to drive it?
If no loss is considered in the flow system, what will be the horsepower (HP) of the motor?
Page No. 3
Fig. for Q. No. 6(c)
7. (a) Water at 20°C exits to the standard sea-level atmosphere through the split nozzle shown in Fig (20)
for Q. 7(a). Duct areas are A1 = 0.02 m2 and A2 = 0.008 m2. If p1 = 135 kPa (absolute) and the
flow rate is Q2 = Q3 = 275 m3/h, compute the force on the flange bolts at section 1.
Fig. for Q. No. 7(a)
(b) Distinguish between ‘differential approach’ and ‘integral approach’ for the solution of fluid
(15)
dynamic problems. Derive the general form of continuity equation in ‘differential approach’.
8. (a) A fluid flow has velocity components of u = 3y2 m/s and v = 6xy m/s, where x and y are in
(10)
meters. What is the acceleration of a fluid particle at (1 m, 2 m)? Is the flow steady or unsteady?
(b) The 100 kg plate in Fig. for Q. 8(b) is resting on a very thin film of SAE 10W-30 oil which has a
(10)
viscosity of μ = 0.0652 Pa.s. Determine the force P that must be applied to the center of the
plate to slide it over the oil with a constant velocity of 0.2 m/s. Assume the oil thickness is 0.1
mm, and the velocity profile across the thickness is linear. The bottom of the plate has a contact
area of 0.75 m2 with the oil.
Fig. for Q. No. 8(b)
(c) The two tanks A and B are connected using a manometer as shown in Fig. for Q. 8(c). If oil is
(15)
poured into tank A to a depth of h = 1.25 m, determine the pressure of the trapped air in tank B.
Air is also trapped in line CD as shown. Take ρoil = 900 kg/m3, ρwater = 1000 kg/m3.
Fig. for Q. No. 8(c)
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