工程流体力学英文试题

英文习题

1.

A

pump

delivers

water

against

a

head

of

l5m

of

also

raises

the

water

from

a

reservoir to the pump against a suction head equal to 250mm of mercury. Convert

these

heads

into

N/m

2

and

find

the

total

head

against

which

the

pump

works

in

N/m

2

and

in

metres of water.

(147kN/m

2

, 33.4kN/m

2

, 180.4kN/m

2

, 18.4m)

cylinders

with

pistons

are connected by

a

pipe containing

water. Their diameters

are 75mm and 600mm and the face of the smaller piston is 6m above the larger. What force

on

the

smaller

piston

is

required

to

maintain

a

load

of

3500kg

on

the

larger

piston?

(276N)

is the atmospheric pressure in N/m

2

if the barometer reading is 750mm of mercury?

What

would

be

the

height

of

the

column

of

water

required

to

produce

this

pressure?

(10

5

N/m

2

, 10.2m)

the foot of a mountain a mercury barometer reads 740mm and a similar barometer at

the

top

of

the

mountain

reads

590mm.

What

is

the

approximate

height

of

the

mountain,

assuming

that

the

density

of

air

is

constant

and

equal

to

1.225kg/m

3

?

(1670m)

Fig. 1 fluid A is water and fluid B is mercury (sp. gr.13. 6). What Will be the difference

in level h. if the pressure at X is 140kN/mz and a= 1.5m?

Fig. 1. fluid A is oil (. 0.8) , flaid B is brine (sp. gr.1.25). If a=2. 5 m and h=0.3m

what

are

(a)

the

pressure

head,

and

(b)the

pressure

in

N/m

2

at

X?

(-2.03m

of

oil,

-15.9kN/m

2

gaug)

7. Assuming that the atmospheric pressure is 101.3kN/m

2

find the absolute pressure at X in

Fig.2-2 when(a) Fluid A is water, fluid B is mercury (.13.6),a=lm and h=0.4,(b) Fluid A

is oil (sp. gr.0.82), fluid B is brine (.1.10), a=20cm and h=55cm.

((a)38.2kN/m

2

, (b)93.8kN/m

2

)

1

oil and

mercury manometer consists of a U-tube 5mm diam with both limbs vertical.

The right-hand limb is enlarged at its upper end to 25mm diam. The enlarged end contains

oil

with

its

free

surface

in

the

enlarged

portion

and

the

surface

of

separation

between

mercury and oil is below

the enlarged end. The left-hand limb contains

mercury only,

its

upper

end

being

open

to

the

atmosphere.

The

right-hand

side

is

connected

to

a

vessel

containing

gas

under

pressure

and

the

surface

of

separation

is

observed

to

fall

2cm.

Calculate the pressure of the gas in N/m

2

if the specific gravity of mercury and oil are 13.6

and

0.85

respectively.

The

surface

of

the

oil

remains

in

the

enlarged

ends.

(0.00517N/m

2

)

9.

In

Fig.3

fluid

A

is

water

and

fluid

B

is

mercury(.1.36).If

the

pressure

difference

between M and N is 35kN/m

2

, a=lm and b=30cm,what is the difference of level h?

(30.7cm)

10. In Fig.3 fluid A is oil (.0.85)and fluid B is a=120cm, b=60cm and h=45cm,

what is the difference of pressure in kN/m

2

between M and N?

(-5.23kN/m

2

)

11. In Fig.4 fluid A is water and fluid B is oil (.0.9). If h is 69cm

and z is 23cm, what

is the difference of pressure in kN/m

2

between M and N?

(-1.57kN/m

2

)

12.

A

mercury U-tube manometer is used to measure the pressure above atmospheric of water in a

pipe,

the

water

being

in

contact

with

the

mercury

in

the

left-hand

limb.(a)

Sketch

the

arrangement

and

explain

its

action.

(b)

If

the

mercury

is

30cm

below

A(Fig.

5)

in

the

left-hand limb and 20cm above A in the right-hand

limb, what is the gauge pressure at A?

Specific gravity of mercury =13.6.

13. A U-tube manometer (Fig.6) measures the pressure difference between two points A and

B

in

a

liquid

of

specific

weight

w

1

.

The

U-tube

contains

mercury

of

specific

weight

w

2

.

Calculate the difference in pressure if a=l.5m b=0.75m and h=0.5m, if the liquid at A and B

2

is water (w

1< /p>

=9810N/m

3

) and the specific gravity of mercury is 13.6 (so that w

2

=13.6w

1

)

14.

An

inverted

U-tube

manometer

is

used

to

measure

the

difference

of

water

pressure

between two points in a pipe. Sketch the the manometer shown in Fig.7 has

air at the top of the tube,find the difference of pressure between point B and point A, if the

specific weight of water w=9810N/m

3

,h

1

=60cm, h=45cm, and h

2

=180cm.

15.

A

vessel

partly

filled

with

liquid

and

moving

horizontally

with

a

constant

liner

acceleration

has

its

liquid

surface

inclined

at

45

°

.Determine

its

acceleration.

(9.81m/sec

2

)

16. A U-tube has a horizontal part 0.6m long with vertical end the whole tube is

rotated about a vertical axis 0.45m from one end and 0.15m from the other, calculate the

speed

when

the

difference

of

level

between

the

tubes

is

0.25m.

(49.9rev/min)

17.A

cylindrical

vessel,

100mm

in

diam

and

0.3m

high,

contains

water

when

at

rest

to

a

3

depth

of

225mm.

If

the

vessel

is

rotated

about

its

longitudinal

axis,

which

is

vertical

calculate from first principles the speed at which the water will commence to spill over the

edge, and the speed when the axial depth is zero.

(34.4red/s, 48.6red/s)

18. What is the greatest speed in revolutions per

min at which an open

cylindrical tank

0.6m in diam may be rotated about its vertical axis, the tank being 0.9m high and two-thirds

filled with water when stationary, if(a)no water is to spill over the sides, (b) the water spills

over the sides and the bottom of the tank is free of water for a radius of 150mm about the

vertical axis?

(109rev/min,154.5rev/min)

19. A tube AOB has the part OB,300mm long, bent upwards so that the angle AOB is 45

°

.

AO is vertical and the end B is closed. The tube AOB is completely filled with water to a

height of 230mm above O. Find the number of revolutions per min of the tube about the

axis

OA

so

that

the

pressure

at

B

is

the

same

as

the

pressure

at O.

what

is

the

least

pressure in OB and where does this occur?

(91.9rev/min,177mm,150mm from O)

20. A fluid of constant density

flows at the rate of 151itres/sec along a pipe AB of 100mm

diam. This pipe branches at B into two pipes BC and BD each of 25mm diam and a third

pipe BE of 50mm diam. The flow rates are such that the flow through BC is three times the

flow rate through BE and the velocity through BD is 4m/s. Find the flow rates in the three

branches BC, BD and BE and the velocities in pipes AB, BC and BE.

(9.77dm

3

/s,1.96dm

3

/s, 3.26dm

3

/s, 1.91m/s,19.92m/s, 1.66m/s)

is flowing along a pipe with a velocity of 7.2m/s. Express this as a velocity head

in metres of water.

What is the corresponding pressure in

kN/m

2

(2.64m, 25.85kN/m

2

)

22.A pipe of 150mm bore is delivering water at the rate of 7500dm

3

/min at a pressure of

820kN/m

2

. It connects by a gradually expanping pipe to a main of 300mm bore which runs

3m above it. Find the pressure in the 300mm main, neglecting losses due to friction.

(814kN/m

2

)

flows from a reservoir into a closed tank in which the pressure is 70kN/m

2

below

atmospheric.

If

the

water

level

in

the

reservoir

is

6m

above

that

in

the

tank,

find

the

velocity of the water entering the tank, neglecting friction.

(16.05m/s)

24.A

pipe

300m

long

tapers

from

1.2m

diam

to

0.6m

diam

at

its

lower

end

and

slopes

downward at 1 in 100. The pressure at the upper end is 69kN/m2. Neglecting friction losses,

find the pressure at the lower end when The rate of flow is 5.5m

3

/min.

(98.5kN/m

2

)

25. The diameter of a pipe changes gradually from 150mm at a point A,6m above datum,to

75mm

at

B,3m

above

pressure

at

A

is

103kN/m

2

and

the

velocity

of

flow

is

4

3.6m/s. Neglecting losses,determine the pressure at B.

γ

=9800N/m

3

(35.3kN/m

2

)

26. A pipe, whose axis is horizontal, is full of water in a section A the velocity of

the water is 90m/min

and the pressure is 138kN/m. If the pipe

tapers

gradually from

150mm diam at A to 100mm diam at B,determine the pressure of the water at B, assuming

that there is no loss of must be the diameter of the pipe at B if the pressure

there is reduced to 27.6kN/m

2

?

(133kN/m

2

47.6mm)

27. A vertical pipe carrying liquid of .0.83 upwards from a pump contracts gradually

from 105mm diam to 35mm diam over a length of 0.45m. A water U-tube is connected to

two points 0.6m apart in the two sections of the pipe and the head

difference registered is

connecting

pipes to the U-tube are filled

with the liquid that is flowing. Find

the rate of flow in dm

3

/min. Ignore losses of energy.

(76.4dm

3

/min)

28.

Water

flows

out

of

a

tank

through

a

siphon

formed

by

a

bent

pipe

ABC,

25mm

in

water in the rank is 1.5m deep and the end of the pipe A is 0.3m above the bottom

of the tank. The length of pipe AB is vertical and is 8.7m long, while BC is 17.4m long. The

pipe discharges into the atmosphere at C, 3m below the bottom of the tank.

Assuming that the barometric pressure is equivalent to 10.2m of water and that the

loss of head in friction is 40v

2

/2g, where v is the velocity of flow in the pipe, calculate the

rate of discharge and absolute pressure at B.

(0.72dm

3

/s, 1.13m of water)

29. Water is siphoned out of a tank by means of a bent pipe ABC 24m long and 25mm diam.

The end A is below the water surface and 150mm above the base of the length AB

is vertical and 9m long and BC is 15m long with the discharge.

30. A vertical

pipe

conveying

water tapers from 50mm in diam at the top to 25mm in

diam at the bottom in a length of 1.8.

A pressure gauge is connected

at the top section

and a second

gauge is fitted at the bottom section. When 0.194m

3

of water per min

flow

up the pipe the gauges show a pressure difference of 31kN/m

2

. Determine the quantity of

water which must flow downwards through the pipe if the gauges are to show no pressure

difference and the frictional losses are assumed to vary as the square of the velocity.

(lll.5dm

3

/min)

31. In a vertical pipe conveying water,

pressure gauges are inserted at A and B where the

diameters are 150mm and 75mm respectively. The point B is 2.4m

below A and when the

rate

of

flow

down

the

pipe

is

21dm

3

/s

the

pressure

at

B

is

12kN/m

2

greater

than

at

A.

Assuming that the losses in the pipe between A and B can be

expressed as kv

2

/2g where v

is the velocity at A, find the value of k.

If the gauges at A and B are replaced by tubes filled with water and connected

to a

U-tube containing mercury of sp. gr.13.6, give a sketch showing how the levels

in the two

limbs differ and calculate thevalue of this difference measured in millimetres.

5

(35.3, 93.6mm)

32. A pump draws water through a 150mm diam pipe from a reservoir whose surface level

is at datum level and discharges it through a 100mm pipe to another reservoir whose surface

level is 72m above datum level. The pump is situated 6m below datum.

The loss of head

in the 150mm suction pipe is 3 times the velocity head in the 150mm pipe and the loss of

head

in

the

100mm

delivery

pipe

is

20

times

the

velocity

head

in

the

100mm

pipe.

Calculate the power output of the pump and the pressure heads at the inlet and outlet of the

pump when the discharge is (a) 0.91m

3

/min,

(b) 2.73m

3

/min.

((a)ll.28kw, 5.85m, 81.61m,

(b)47.4kw, 4.65m,

l10.5m)

33.

A horizontal venturi meter measures the flow of oil of specific gravity 0.9 in a 75mm

diam pipe line.

If the

difference of pressure

between the full bore and throat tappings

is 34.5kN/m

2

and the area ratio m is 4, calcculate the rate

of flow, assuming a coefficient

of discharge of 0.97.

(a =0. 0106m

3

/s)

34.

Derive an expression for the rate of flow through an inclined venturi

meter and show

that,

if

a

U-tube

type

of

gauge

is

used

to

measure

the

pressure

difference,

the

gauge

reading will be the same for a given discharge irrespective of the inclination of the meter.

A vertical venturi meter measures the flow of oil of specific gravity 0.82, and has an

entrance

of

125mm

diam

and

a

throat

of

50mm

are

pressure

gauges

at

the

entrance and at the throat which is 300mm above the entrance. If the

coefficient for the

meter is 0.97 find the flow in m

3

/s when the pressure difference is 27.5kN/m

2

.

(Q = 0.01535m

3

/s)

35.

The

velocity

distribution

in

a

circular

piper

of

radius

R

can

be

expressed

as

?

y

?

u

?

0

?

?

.

where

u

is

the

velocity

at

a

point

distant

y

from

the

wall

and

u

0

is

the

?

R

?

6

1

m

velocity at the axis.

Demonstrate

that

if

a

pitot

tube

is

placed

at

0.25R

from

the

wall,

the

pitot

registers

the

correct mean velocity within ±

0.5 percent for a range of m from 4 to 10.

Find the kinetic energy per unit weigh of flow in terms of the mean velocity when m=7.

?

v

2

?

?

1.056

?

2

g

?

?

36.

A

venturi

meter

measures

the

flow

of

water

in

a

75mm

diam

difference of head between the throat and the entrance of the meter is measured by

a U-tube containing mercury, the mercury being in contact

with the water. What

should be the diameter of the throat of the meter in

order

that the difference in

level of the mercury be 250mm when the quantity of water flowing in the pipe is

620dm

3

/min? Assume a coefficient of discharge of 0.97.

(40.7mm)

37. A venturi meter fitted to a pipe of 450mm bore has a throat diameter of 200mm. Find the

quantity

of

water

flowing

when

the

venturi

head

is

175mm

of

water.

Take

C

d

?

0.96< /p>

.

(0.057m

3

/s)

38. A venturi meter installed in a horizontal water main has a throat diameter of 75mm and a

pipe diameter of coefficient of discharge is 0.97.

Calculate the rate of flow in

the main in m3/h if the difference of level in a mercury U-tube gauge connected to the

throat and full bore tappings is 178mm,the mercury being in contact with the water.

(106.5m

3

/h)

39. A venturi

meter

having an entrance

diameter of 300mm and a throat diameter of

200mm

is

used

to

measure

the

volume

of

gas

flowing

through

a

pipe.

The

discharge

coefficient is 0.96. Assuming the

density of the gas to be constant and equal to 0.99kg/m

3

,

calculate the volume flowing per sec when the pressure difference

between entrance and

throat as measured on a water U-tube gauge is 61mm. Prove any formula used for the meter.

(1.17m

3

/s)

40. The throat and full bore diameters of a venturi meter are 19mm and 57mm respectively.

Calculate the coefficient of discharge of the meter if the pressure at the full bore section is

172.5kN/m

2

above

that

at

the

throat

when

the

meter

is

passing 311dm

3

/min

of

7

centeline of the meter is inclined to the horizontal,the throat section being 0.46m above the

full bore section.

(0.99)

41.

A

venturi

meter

has

its

axis

vertical,the

inlet

and

throat

dia-

meters being 150mm and 75mm respectively. The throat is 225mm above the inlet and the

coefficient of discharge is 0.96. Petrol of .0.78 flows through the meter

at the rate of

39.6dm

3

/s. By application of

Bernoulli’s principle, find:

(a) the pressure difference in kN/m

2

between inlet and throat;

(b)

the

difference

of

level

which

would

be

registered

by

a

vertical

mercury

manometer, the tubes above the mercury being full of petrol.( of mercury

=13.6)

(34kN/m

2

, 0.257m)

42. A venturi meter in a horizontal 300mm diam water pipe has a throat diameter of 100mm

and a discharge coefficient of 0.98. A mercury U-tube was used to measure the difference

of head between the pipe inlet and the throat at points 0.6m apart.

If the mercury gauge

reading

was

760mm,

find

the

flow

through

the

pipe

in

dm

3

/s.

The

connections

to

the

U-tube are filled with water:

If the meter had been placed vertically with the flow upward, what would have been

the gauge reading for the same rate of flow?

(106.2dm

3

/s, 760mm)

43. A pitot-static tube placed in the centre of a 200mm pipe line conveying water has one

orifice

pointing

upstream

and

the

other

perpendicular

to

it.

If

the

pressure

difference

between the two orifices is 38mm of water when the discharge through the pipe is 22dm

3

/s,

calculate the meter coefficient. Take the mean velocity in the pipe to be 0.83 of the central

velocity.

(0.977)

44. Obtain an expression for the velocity in terms of the observed difference

in level of

the

liquid,of

specific

gravity

S,

in

the

U-tube

connected

to

the

up

and

down-stream

orifices of a pitot tube immersed in flowing

the difference of level is 0.36m, the

speeific

gravity

of

the

liquid

1.25

and

the

calibration

coefficient

for

the

orifices

0.865,

what is the velocity in m/s?

(0.813m/s)

45. A pitot-static tube is

located in the centre of an air duct to measure the velocity on the

duct axis. An inclined manometer containing fluid of relative

density 0.785 is connected

to

the

pitot- static

tube

to

measure

the

pressure

difference

between

the

the

inclined tube of the manometer makes an angle of 15deg with the horizontal and the ratio of

the

diameters

of

the

enlarged

vertical

tube

to

the

inclined

tube

is

5,

find

the

decrease

in

velocity

in

the

duct

if

the

manometer

deflection

along

the

inclined

tube

decreases

from

150mm to 100mm.

46.

Sulphurie

acid

of

specific

gravity

1.3

is

flowing

through

a

pipe

of

50mm

internal

diameter.

A

thin- lipped

orifice,

10mm

diameter,

is

fitted

in

the

pipe

and

the

differential

pressure

shown

by

a

mercury

manometer

is

10cm.

Assuming

that

the

leads

to

the

8

manometer

are

filled

with

the

acid,calculate

(a)

the

weight

of

acid

flowing

per

second,

and(b)the approximate loss of pressure (in kN/m

2

) caused by the orifice.

The coefficient of discharge of the orifice may be taken as 0.61 the specific gravity of

mercury as 13.55,and the density of water as 1000kg/m

3

.

(a) G=0.085kg/s

(b) 1.2kN/m

2

)

47. Molten slag is passed over a matte in the smelting of copper in order to recover most of

the copper in the slag. The operation is carried out in a reverberatory

furnace 80ft long

and 30ft wide. Assuming that the matte is stationary (in reality this is oversimplified) and

that the slag flows continuously (80ft

3

/hr) over the matte, determine: (a)the equation for the

velocity distribution in the slag layer; (b) the fraction of material which stays in the furoace

for

a

period

twice

the

mean

residence

time

and

longer.

The

average

depth

of

the

slag

may

be taken as 2ft.

x

2

(

V

z

?

2

?

,0. 185)

2

48. Consider the fully developed flow of a fluid in a long tube of length L and radius R; we

specify fully developed flow so that end effects are negligible. Since we are dealing with a

pipe it is convenient to work with cylindrical coordinates.

Therefore the shell in

Fig.11

is cylindrical, of thickness

△

r and length L.

Find the solution for the velocity distribution:

2

2

?

P

o

?

P

L

?

?

R

?

?

?

r

?

?

?

?

< br>g

?

?

?

?

1

?

?

?

?

v

z

?

?

L

?

?

?

4

?

?

?

?

?

< br>R

?

?

?

And

i) The maximum velocity is at r=0,and is given by

V

max

z

2

?

P

o

?

P

L

?

R

?

?

?

< br>?

g

?

?

L

?

4

?

ii)The average velocity is

1

v

z

?

?

R

2

iii)V

olume flow rate is

2

x

R

2

?

P

o

?

P

L

?

R

v

z

rdrd

?

?

?

?

g

?

?

?

L

8

?

?

?

0

0< /p>

9