Solutions to ME3122 Quiz 2 Question 1
Water at 20 C flows inside a tube of diameter 50mm and length 20 m at a rate of 6 kg/s. The pressure drop along the pipe is measured to be 41 kPa. Determine the friction factor and thence estimate the heat transfer coefficient between the tube and the water. The properties of water
may be evaluated at 20 C.
(35 Marks)
20m
Solution:
Given pressure drop,
o
20 C @ 6kg/s
From saturated water-steam table o
@ 20 C
3 m /kg
, , Pr =6.95,
. ̇ ̅ ̇ ̅ ̅ ( ) = 3.0613 m/s
Therefore,
> 2000 (Turbulent flow) Using Darcy eqn for pipe flow,
,
( ̅ )
Using the Reynolds-Colburn analogy for heat tran sfer in turbulent flow in pipes,
,
where,
Therefore, ̅
Question 2
For laminar flow of a fluid of constant properties over an isothermal flat plate of surface temperature and length L, if the free stream velocity is doubled, how much would the heat transfer rate from the plate be increased by, b y, assuming that the flow is still laminar despite the increased velocity? (25 Marks) Solution: 1
1
Nu L 0.664 Re L 2 Pr 3
Therefore,
u L 0.664 k
h L L
1
2
1
Pr 3
Let u 2 2u h L 2
Therefore,
2u L 0.664 k
h L2 L
1
2
Therefore,
1
Pr
3
1
u L 2 1 2 0.664 Pr 3 2 h L 1.414 hL k
h L 2 L
Therefore, h L is increased by 41.4%
Since, q h L T w T and T w T constant "
"
Therefore, q is increased by 41.4%
Question 3
Oil flows at a rate of 0.02 kg/s inside a 4-m-long, 40mm x 10mm rectangular conduit which is 2
heated by a uniform wall heat flux of 1000 W/m . The inlet temperature of the oil is 50 C. The
properties of the oil are given as follows and assumed to be constant:
0.032 kg/m.s,
c p 2130 J/kg.K, k 0.14 W/m.K,
850 kg/m
3
and Pr 487.
Assuming hydrodynamically and thermally fully developed flow, determine the average heat transfer coefficient between the conduit and the oil, and the outlet temperature of the oil. (40 Marks) Solution:
D H
4 0.04 0.01
0.1
0.16 m
L 4 m
Au 850 0.04 0.01 u 0.02 kg/s m u 5.88 10 2 m/s.
Re
u DH
850 5.88 10 2 0.016 0.032
Nu D
h
hDH k
25.0 2000 (Laminar F low)
4.44
4.44 0.14 / 0.01 016 6
2
38.85 W/m K
2
q" 1000 W/m
q q" A 1000 2 ( 0.04 0.01 ) 4 400 400 W q
c p ( T b2 m
T b 2
50
T b1 )
400 400 W
50 9.4
400 0.02 2130
O
59.4 C
