Solutions to ME3122 Quiz 2

Question 1

Water at 20C 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 20C.

(35 Marks)

Solution:

Given pressure drop,

From saturated water-steam table

@ 20oC

m

3/kg

,

,

Pr =6.95,

.

( ) = 3.0613 m/s

Therefore,

> 2000 (Turbulent flow)

Using Darcy eqn for pipe flow,

,

( )

20 oC @ 6kg/s

20m

Using the Reynolds-Colburn analogy for heat transfer 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, assuming that the flow is still laminar despite the

increased velocity?

(25 Marks)

Solution:

31

21

6640 PrRe.Nu LL

Therefore, 312

1

6640 PrLu

.k

LhL

Let 22 2 Lhuu

Therefore, 312

1

2 26640 Pr

Lu.

k

LhL

Therefore,

LL

L h.hPrLu

.k

Lh4141266402 3

121

2

Therefore, Lh

is increased by 41.4%

Since,

TThq wL" and constant TTw

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

heated by a uniform wall heat flux of 1000 W/m2. The inlet temperature of the oil is 50C. The

properties of the oil are given as follows and assumed to be constant:

487.Pr and kg/m 850 W/m.K,140 J/kg.K, 2130kg/m.s, 032.0 3 .kcp

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:

m 16010

0100404.

.

..DH

m 4L

m/s. 1088.5

kg/s 02.001.004.0850

2

u

uuAm

low)(Laminar F 02000250320

016010885850 2

..

..DuRe H

444 .k

hDNu H

D

KW/m 85380160140444 2../..h

2W/m 1000"q

W 400401004021000 )..(A"qq

W 400 12 )TT(cmq bbp

C45949502130020

40050 O

2 ...

Tb