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GROUP MEMBERS

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No Name Id Programe

01 Lipon islam 14207082 BSME

02 Jilani al mamun 14207099 BSME

03 Rashedujjaman 14207069 BSME

04 Nazmul Hossain 14207088 BSME05 ALamin 13107061 BSME

TOPIC

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Flow Through Simple pipesAnd Flow through compound pipes

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CONTENTS: Flow through simple pipes Loss of head in pipes Darcy’s formula for loss of head in pipes Chezy’s formula for loss of head in pipes Transmission of power through pipe Time of emptying a Tank through a long pipe Flow through compound pipes Discharge from one reservoir to another through a pipe

line Discharge through a compound pipe Discharge through pipes in parallel

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LOSS OF HEAD IN PIPES Whenever the water is flowing in apipe ,it experiences some resistance to its motion,whos efect is to reduse the velocity and ultimately the head of water available .though there are many types of losses ,yet the major loss is due to frictional resistance of the pipe only.the frictional resistance of the pipe depends upon the roughness of the inside surface of the pipe,grseater will be the resistance .this friction is known as fluid friction and the resistance is known as frictional resistance . the earlier experiment on the fluid friction were conducted by froude we concluded on that 1.The frictional resistance varies approximately with the square of thee velocity of the liquid.2.The frictional resistance varies with the name of the surface lare on ,some empirical formula were derived for the loss of head due to the friction out of which following two are important from the subject point of view.3.dercy’s formula for loss of head in pipes and4.chezy’s formula for loss of head in pipes

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DARCY’S FORMULA FOR LOSS OF HEAD IN PIPE

Fig: uniform long pipe

Consider a uniform long pipe through which is flowing at a uniform rate.

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Let, l = length of pipe d = diameter of a pipe v = velocity of water in the pipe

f' =frictional resistance per unit area per unit velocity

let us consider sections (1-1) and (2-2) of the pipe . Now let

Now considering horizontal forces on water between sections (1-1) and (2-2)and equating the same ,

or frictional resistance = =

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= But , = hf = loss of pressure head due to friction

=

We know that as per froudes experiment frictional resistance

f

substituting the value of friction resistance in the above equation =

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let us introduce another coefficient (

=We know that the discharge Q=

Substituting the value of

=

CHEZY'S FORMULA FOR LOSS OF HEAD IN PIPES:Consider a uniform long pipe through which water is following at a uniform rates shown in fig:LetI = Length of the pipe andD = Diameter of the pipeArea of pipe ×And perimeter of pipe P = dV = velocity of water in pipef = Frictional resistance, per unit area of v'etted surface per unit velocity and, Loss of head due to fricationNow let us consider section (1-1) and (2-2) of the pipe Let, = intensity of pressure at section 1 –land P2= Intensity of pressure at section 2,2

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A LITTLE CONSIDERATION WILL SHOW THAT P1 AND P2 WOULD HAVE BEEN EQUAL , IF THERE WOULD HAVE BEEN NO FRICTIONAL RESISTANCE . NOW CONSIDERING HORIZONTAL FORCES ON WATER BETWEEN SECTIONS 1-1 AND 2-2 AND EQUATING THE SAME , OR, FRICTIONAL RESISTANCE=A

OR, =OR, =-

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But , − = = loss of pressure head due to friction ℎ𝑓=

We know that’s experiment , frictional resistance=frictional resistance per unit area at velocity × wetted area×=f´×Substituting the value of frictional resistance in the above equation == (=×

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Now substituting another term of hydraulic mean depth in the above equation ,such that hydraulic mean depthm== =×

= ×m×

V= ……(1)Now substituting two more terms in the above equation such thatC=c Now substituting the above two values in equation (1)V=c

Transmission of Power through a Pipe

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Whenever water is allowed to fall from higher level to lower level , we can always generate some power as a matter of fact ,whenever we come across a waterfall, we do not allow the water simply to fall. But it is made to follow through a pipe , so that the direction of the water may be set in some convenient way from which we may produce some power . A little consideration will show that some hade of water will be lost due to friction in the pipe through which the water is flowing

Fig: transmission of pipes

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Consider a high level strong tank .let a pipe AB lead water from this tank from A to a power house at B as shown in figure:

=Hade of water at a power house AB in meters = length of the pipe AB in metre = velocity of water in the pipe in m/s =loss of heat in the pipe AB due to friction in meters coefficient of friction, and d=diameter of the pipe AB in meters

Cross-sectional area of the pipe, We know the weight of water flowing per second ` 

η (AS ) And net head of water available at (neglecting minor losses)Efficiency of transmission, we also know that power available, Weight of water flowing per second Head of water .

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A little consideration will shown that, in that above equation, the power transmitted depends upon the velocity of water (v),as the other things are constant. Therefore the power transmitted will be maximum when

Or when the differential coefficient of the amount inside the bucket of equation ( is zero . i e Or Or as ( Or It means that the power transmission through a pipe is maximum, when the head lost due to friction in the pipe is equal to 1/3 of the total supply head.

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TIME OF EMPTYING A TANK THROUGH A LONG PIPE

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Consider a tank, which is to be emptied through a long pipe as shown in fig.Let, = Initial head of water, in the tank, before opening the pipe,= Final head of water, in the tank, after opening the pipe in T seconds,(-) =Fall of water level in the tank,A (-) = Volume of water discharged through the pipe,l = Length of the pipe,d= diameter of the pipeT=time taken in seconds , to fall the water level in the tank from to

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Consider an instant, when the head of water in the tank is h. After a small interval of time dt, at the water level in the tank fall down by an amount equal to dh. Volume of water that has passed through the pipe in the time dt = -Adh ……. (1)(Minus value of dh is taken, as the value of h decreases as the as the discharge increases). Since the water is being discharged in the atmosphere, therefore (ignoring all other losses except friction) there will be some loss of head of water at outlet also.

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h = = (1+ )v=In time dt, the volume of water that has pass through the pipe =Area of pipe ×velocity of water ×time= × ×dt …………..(2)Equating equation (1) and (2)-Adh= × ×dt

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dt= =Now the total time T, required to bring the water level from may be found by integrating the equation between the limits i,e…T=We have seen that the velocity of water v =

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Velocity of water when the head of water average velocity = == ×()T= dh = = ×()

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Taking minus out of the bracket,T= ×() If the tank is to be completely emptied ,then substituting =0,in the above equationT= ×

DISCHARGE FROM ONE RESERVOIR TO ANOTHER THROUGH A PIPE LINEsometimes ,discharge from one reservoir to another takes place through a pipe line.in such a case ,It is assumed that the difference between the water levels of the two reservoir is lost due to friction in the pipe in the line . we can discuss the discharge from one reservoir to another through-1.Compound pipes2.Pipes in parallel3.Branched pipes and4. Siphon pipes

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DISCHARGE THROUGH A COMPOUND PIPE(I.E PIPES IN SERIES) Sometimes while laying a pipeline ,we have to connect pipes of different lengths and different diameters with one another to from a pipe line . such a pipe line is called a compound pipe or pipes in series .a little consideration will show that as the pipes are in series ,therefore the discharge will be continuous.Now consider a compound pipe discharge water from one tank with a higher water level to another with a lower water level as shown fig.

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Let,Q=discharge through the pieH=total loss of head diameter of pipe 1=length of pipe 1=coefficient of friction of pipe 1=corresponding value of pipe 2=corresponding value of pipe 3 and so onNeglecting minor losses except friction , we know that the total loss of head,H=loss of head in pipe 1+loss of head in pipe 2+loss of head in pipe 3 =++…. =(++…..)

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If the coefficient of friction is the sum for all the pipes,thenH=( ++……)If the discharge through the pipe line is given then the total loss of headH=+++………

=(+++………)If the coefficient of friction is the same for all pipes,thenH==(+++………)

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DISCHARGE THROUGH PIPES IN PARALLEL

Sometimes in order to increase the discharge from one tank into another , anew pipe has to be laid along with the existing one . such an arrangement is known as pipes in parallel as shown in fig.

fig: pipes in parallel

A little consideration will show that as the pipes are parallel, therefore the loss of head for all the pipes will be the same and all the pipes will discharge water idependently .the total discharge through all the pipes will be the same of discharge in the various pipes.

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