流体力学与传热习题参考解答(英文)

1. Water is pumped at a constant velocity 1m/s from large reservoir resting on the floor to the open top of an absorption tower. The point of discharge is 4 meter above the floor, and the friction losses from the reservoir to the tower amount to 30 J/kg. At what height in the reservoir must the water level be kept if the pump can develop only60 J/kg?

2222112f 1U P U P w=Z g+h (Z g+)22ρρ

++-+ U 1=0 12P =P 10Z = W=60j/kg f h 30/kg =

2U =1m/s 2(60300.5)/g 3m Z =--=

21Z Z Z 431m ?=-=-=

2. The fluid (density 1200 kg/m 3 ) is pumped at a constant rate 20 m 3 /h from the large reservoir to the evaporator. The pressure above the reservoir maintains atmosphere pressure and the pressure of the evaporator keeps 200 mmHg (vacuum). The distance between the level of liquid in the reservoir and the exit of evaporator is 15 meter and frictional loss in the pipe is 120 J/kg not including the exit of evaporator, what is the pump effective work and power if the diameter of pipe is 60 mm?

22112212f U U Z g+

W Z g+h 22

ρρP P ++=++ 10P = 5422200P x1.013x10 2.67x10N /m 760

=-=- 31200Kg /m ρ= 1U 0= f h 120J /kg =

22V 20U 1.97m /s A 3600*4006===π/*.

1Z 0= 2Z 15=

2.67x101.97W 15x9.81120246.88J /kg 12002

=-+++= N W Q 246.88x1200x20/3600=1646W ρ==

3. Water comes out of the pipe (Φ108x4 mm), as shown in Fig. The friction loss of the pipeline which does not cover the loss at the exit of pipe can be calculated by the following equation:

h f =6.5U 2

where U is the velocity in the pipe, find

a. water velocity at section A-A'.

b. water flow rate, in m 3 /h.

221

12212f U U Z g+Z g+h 22ρρP P +=++

1U 0= 12P =P 1Z 6m = 2Z 0= 2f h 6.5U = 22U 6x9.81 6.5U 2=+

U 2.9m/s = 23V=UA=2.94x01

x360082m /h =π/. 4. Water passes through the variable pipe. The velocity in the small pipe is 2.5 m/s. The vertical glass tubes are inserted respectively at the section A and B to measure the pressure (see fig.) If the friction loss between two section is 15 J/kg, what is the water column difference between two glass tubes? By the way, draw the relative liquid column height of two tubes in the Fig.

a a

b b U A U A = 2b U 2.5*(33/47)1.23m /s ==

22a a b b a b f U U Z g+Z g+h 22

ρρP P +=++ a b Z =Z 22a b b a f U U h 22

ρρP P -=-+221.23/2 2.5/21512.63=-+= a b P P R g ρ-=? 3312.63R=1.29x10m 9.8x10

-?=

5. A centrifugal pump takes brine (density 1180 kg/m 3 , viscosity 1.2 cp) from the bottom of a supply tank and delivers it into another tank. The line between the tanks is 300 m of 25 mm diameter pipe (inner diameter). The flow rate is 2 m 3 /h. In this line, there are two gate valves, four elbows (90o ) and one return bend, what is the friction loss if the roughness of pipe is 0.025 mm?

22f fst flocal U U h h h 4f k d 22

l ∑=+=+∑ 31180kg /m ρ= 300m, d=0.025m l =

3-3v 2m /h =1.2cp=1.2x10Pa.s μ=

k=0.025mm k/d=0.025/25=0.001

c l r k =0.4 k =1 k =2x0.07=0.14

el re k 4x0.75 3 k 1.5-2.2===

2u v /A 2/(3600x /4x0.025)1.13m /s π===

4u d Re 2.78x10ρμ

== f 0.063= 2f 2h 4x0.0063x300/0.025x1.13/2+

(0.4+1+2x0.07+4x0.7+1.5)x1.13/2 =197.86J/kg

∑=

6. The orifice meter (diameter of orifice 0.0001 m) is installed for measuring the flow rate. The indicating liquid of orifice is mercury if U shape pressure gauge reading is 0.6 meter and orifice coefficient can be taken as 0.61, what is the flow rate of water?

0o o 2gR()u c ρρρ-=

20o 02gx0.6x(136001000)

V u s 0.61x /4x0.0001x 1000π-== 835.8x10m /s -=

7. Water flows through a pipe with a diameter di 100 mm as shown in figure.

a. when the valve is closed, R is 600 mm and h equals 1500 mm. While the valve opens partially, R=400 mm and h=1400 mm, f=0.00625 (Finning factor) and k c =0.5 (contraction coefficient), what is the flow rate of water, in m 3 /h?

b. If the valve opens fully, what is the pressure of section 2-2', in N/m 2 ? The equivalent length of the valve is 1.5 m and the Fanning factor f keeps the same?(ρH2O =1000kg/m 3, ρHg =13600kg/m 3)

(1) the valve opens partially ,for selection 1-1’ and 2-2’ , we have 22112212f1-2u u gZ gZ h 22ρρ

P P ++=+++ 2212Hg H o 0 g(R h)39630N/m ρρP =P =-=

2212f1-2c u u u 0 Z =0 h 4f +k 2.13u d 22

===l We can get Z1 from the valve closed

21Hg H O h=1.5m R=0.6m Z gR/h 6.66m ρρ=-=

229.81x6.66u /2 2.13u 39630/1000=++

23h u=3.13m/s V 3600x /4x0.1x3.1388.5m /h π==

(2) when the valve opens fully, for section 1-1’and 3-3’, we have

13f1-3

gZ gZ h

ρρ

++=+++

311

Z0 Z 6.66m u=0

f1-3c

u 3.1.5

h(4f k)(4x0.00625x+0.5) 4.81u

d20.01

l l++

=+==

9.81x6.66u/2 4.81u

=+u 3.51m/s

For section 1-1’and 2-2’

1122

12f1-2

u u

gZ gZ h

ρρ

P P

++=+++

11212

0 Z 6.66 Z0 u0 u 3.51

P=====

f1-2c

l u

h(4f k)(4x0.00625x15/0.10.5)3.51/226.2J/kg

=+=+=

9.81x6.66 3.15/226.2

32970

=++

8. The rotameter is installed to measure the water flow rate, as shown in figure. If the total length including equivalent length of pipeline A is 10 m and the reading of rotameter is 2.72 m3 /h, what is the flow rate for pipeline B? (f A =0.0075, f B =0.0045)

For parallel pipe line

fA fB total A B

fA A2

h h V V+V

(l+le) 2.72

h4f4x0.0075x10/0.053/2()

d23600x/4x0.053

∑=∑=

∑

∑==

0.333J /kg =

22B fB B B B 23B B B B u (l+le)h 4f 4x0.0045x2/0.3/2xu 0.333d 2u 2.36m /s V =u A 2.36x /4x0.23600m /h π∑∑======

10. A flat furnace wall is constructed of 120 mm layer of sil-o-cel brick, with a thermal conductivity 0.08 w/(m o C), backed by a 150 mm of common brick, of conductivity 0.8 w/(m o

C), the temperature of inner face of the wall is 1400 o , and that of the outer face is 200o C. a. What is the heat loss through the wall in w per square meter.

b. To reduce the heat loss to 600 w/m 2 by adding a layer of cork with k 0.2 w/(m o C) on the outside of common brick, how many meters of cork are requied? a. 2Q t 1400200711N /m 11L R 0.080.8

0.120.15

∑?-===∑+ b. 600=(1400-200)/(0.12/0.08+0.15/0.8+x/0.2)

x=0.0625m

13. Air at the normal pressure passes through the pipe (d i 20 mm) and is heated from 20o C to 100o C. What is the film heat transfer coefficient between the air and pipe wall if the average velocity of air is 10 m/s? The properties of air at 60 o C are as follows:

density 1.06 kg/m 3 , viscosity 0.02 cp, conductivity 0.0289 w/(m o C), and heat capacity 1 kJ/kg-K

443u d 10x0.02x1.06 Re=1.06x10100.02x10

ρμ-==>

12T +T 20100T=6022+==℃ 0.141ωμμ??= ???

10000.020.0010.6920.0289

p c x x k μ==Pr=

()()0.81/3081/34Nu 0027Re Pr 0.027x 1.06x10x 0.69239.66==.=.

()2i i i h d 39.66 h 39.66x0.0289/0.02=57.22w/m .k k ==