wu2c5 by Adel Khamis

8/14/2019 wu2c5 by Adel Khamis

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Unit two -241- Chapter five

Factors required for the steady flow:

.

.

.

.

Flow rate and the equation of continuity:

To understand what is meant by the flow rate and equation of continuity, two

planes normal to the streamlines at A and B. The cross sectional areas are A and B

respectively.

The volume of the liquid flowing through area A1 is:

V1= . x

The volume of the liquid flow in

unit time is (volume rate flow):

..............

....x..................Q

1=

Q1 = . x ..

The volume of the liquid flowing through area A2 is:

V2 = . x

The volume of the liquid flow in unit time is (volume rate flow):

..............

....x..................Q

2 =

Q2 = . x ..

Since the mass can be calculated as V (density x volume)

Therefore the mass per unit time is: . x . x kg/s

The mass of liquid that passes at the area A1 per unit time is:

Worksheet 2008/2009

A1

A2

S1

S2


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The mass of liquid that passes at the area A2 per unit time is:

Since the mass per unit time passing at the area A1 and A2 are equal therefore

Q(m) = (Qm)

x . x .. = x . x ..

A.V. = A.V

......

......

2

1=

V

V

G.R.:

The blood moves slower in the capillaries than in major arteries although the radius

of capillaries is smaller than that of major artery.

What is meant by?

The rate of flow = 5 kg/ s.

The rate of flow = 5 m3/ s.

Draw a graphical relation between the rate of flow at the y-axes and velocity of flow

at x-axis:

The mathematical relation ..

The slope means .

N.B.:

Q = . In terms of area and velocity.

A1V1= In case of regular tube

A1V1= in case of tube has equal holes at the other end.

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A1V1 = in case of tube has more than one hole

at the other end.

Q = .. in terms of Volume and time.

Examples:

A water pipe entering a home has a diameter of 2 cm, and the speed of water is 0.1

m/s eventually if the pipe becomes of diameter 1 cm, calculate:

a) The speed of water in the narrow portion.

b) The amount (volume and mass) of water that flows per minute across any

cross sectional area.

[0.4 m/sec, 188.4x10-5 m3, 1.884 kg]

In a normal adult, the average speed of the blood through the aorta (of radius 0.7 cm)

is 0.33 m/sec from the aorta the blood goes into the major arteries (the radius of each

is 0.35 cm) which are 30 in number. Calculate the speed of the blood through the

arteries.

[0.044 m/sec]

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A tube has a cross sectional area 10 m2 at A and 2 cm2 at B. If the flow velocity at A

is 12 m/s. find the liquid flow velocity at B.

[60 x 104 m/sec]

A tube provides a field with water, its cross sectional area is 4 cm 2, the velocity of

water is 10 m / s. The end of the tube is closed and contains 100 holes each of area

1 mm2. Find the velocity of flow from each hole.

[40 m/sec]

Gasoline flows in a pipe of diameter 2 cm with velocity 5 m/s. Find the rate of

flow and calculate the time in minutes required to fill a reservoir of volume 20 m3

with gasoline.

[1.57x10-3 m3/sec, 212.2 min]

Oil is pushed with a rate of 6 Liter / minute through a pipe attached to another pipe

from which the oil goes out with velocity of 4 m / s. Calculate the cross sectional area

of the second pipe.

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[0.25 x 10-4 m2]

Enriched notes:

Bernoullis Effect:

The upper side of the airplane wings is .., while the lower side is .

Therefore the air path at the upper surface is (longer / shorter) than that at lower.

That leads to decrease in pressure at the (upper / lower) surface, which makes

difference in pressure to left the airplane upward without falling. That is called

Bernoullis effect.

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Circulatory System:

The total area of capillaries is (greater than/ equal to/ smaller than) the area of the

aorta.

Therefore the blood speed at capillaries is much (slower / faster) than that in aorta.

Hardening of the Arteries:

The and of the arteries muscles controls the blood flow.

The .. on the arteries walls lead to hardening of

the arteries.

Sometimes it form which may case angina.

Sphygmomanometer:

It consists of wounded around the arm.

The pressure increase by using of to stop the blood flow at the

brachial artery.

By decreasing the pressure, the blood start to flow in a turbulent flow, due to

, and that causing sound can be heard by stethoscope, and the

pressure can be measured by using of manometer (..pressure).

By decreasing the pressure in the air bag, the brachial artery completely opened

and the flow of blood becomes .. and the sound vanish, the pressure

can be measured ( pressure).

If systolic pressure increases than mm Hg, it may lead to stroke.

If diastolic pressure increases than .mm Hg, it causes extra effort at the

hart.

Pumps:

Pumps can be classified according to the function into: .. pump and

. pump.

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And it can be classified according to its design into:

a) Reciprocating pump: where; when the piston moves inside the pump, the

pressure of the fluid opens the (outlet /

intake) valve casing the fluid to flow (into/

out of) the pump, and when the piston

moves out of the pump, it open the (outlet/

intake) valve and the fluid (get out/ inter)

the pump. And the heart can be considered

as reciprocating pump.

b) Circulating pump, or centrifugal pump: where the . of the

blades casing the fluid to be pushed, and this kind is used in vacuum cleaner.

Viscosity:

Definition:

Experiment (1):

Suspend two similar funnels to a stand.

Pour suitable volume of in one funnel and same volume of

in the other funnel.

We can notes that the stream velocity of alcohol is (higher / slower) than that of

glycerin.

Experiment (2):

Take two beakers contain a suitable volume of honey and water.

Stir the liquids in the two beaker, with a glass rod, we can notice that:

The glass rod moves in water (easier / harder) than honey.

After taken out the rod, honey stop rotation (faster / slower) than water.

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Experiment (3):

Take two long cylinders, one filled with water, and the other with glycerin.

Drop metallic ball in each of the two cylinders.

The ball in water moves (faster / slower) than that in glycerin.

To explain the concept of viscosity let

us imagine a layer of a fluid confined between

two parallel plates. One of them is at rest and

the other moves with velocity (V), between the

two plates the fluid moves with velocities from

zero (at the lower plate) up to V (at the upper

one).

To keep the plate moving with constant velocity a force F (friction force) is

required. This force depends on:

1. Kind of liquid

2. .. where F ..

3. . where F ..

4. . where F ..

........

...........

.......

..........

.......

...........

=

=

F

F

Where is the coefficient of viscosity.

Coefficient of viscosity of liquid:

Definition: ..

Rule: ...

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Dimensional formula:

Units: . or or .

Factors affects viscosity coefficient:

...

...

...

Applications of viscosity:

Lubrication:

What is meant by lubrication?

.

G.R.:

Water is not used in lubrication.

.

Reducing the consumption of fuel in moving cars:

The relation between the resistance of air to moving cars and the slow velocity:

...

The relation between the resistance of air to moving cars and the high velocity:

..

Then to save the fuel, drivers tend to: ..

Sedimentation rate of blood:

When a body falls freely, it affected by three forces:

a) ............................................ in ..direction.

b) ............................................ in ..direction.

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c) Frictional force due to of fluid.

The final velocity due to the three forces becomes (directly / inversely)

proportional to the radius of the body.

This phenomenon is used in medicine to measure the sedimentation rate,

where the blood poured in a cylinder, and the time of RBC for precipitate is measured:

a) The increase of velocity indicates where the radius

of RBC (increase / decrease) due to the adhere of red corpuscles

b) The decrease of velocity indicates .. where the radius or RBC

(increase/ decrease) decrease, due to .. of the red

blood corpuscles.

What is meant by?

The coefficient of viscosity of water = 0.01 Kg m-1 s-1.

.

G .R.:

It is preferred to drive a car by moderate velocity.

.

Measurement of sedimentation rate.

.

Water is not used in lubrication.

.

Enriched notes:

Syphon phenomenon:

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Liquid can move upward, when it is pulled in a tube bend downward, where

the . force between molecules, held the molecules together to

become like continues membrane or continues chain.

Same occurs with metallic chain in some kinds of livers.

Also it takes place in capillarity tubes, and that is the reason where water

moves upward in trees.

Worksheet 2008/2009

wu2c5 by Adel Khamis

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