Flow Chart of Report

REPORT

Flow Chart of Report

1.Problem Statement

Design a system to supply water flow from the reservoir to the elevated tank shown in below at a discharge of Q= 1.0 m³/s.

1. Approach and Assumptions

Identifying the piping connections of the system and arranging all its auxiliaries from initial to the final discharge. Locating and calculating all the valves, gate valve and all head losses. Assuming, iterating and calculating for the achieving required flow rate at discharge of Q= 1.0 m³/s.

• Result and Discussion

Pipe line Connection:     

As per calculation and iterations based on all head losses considering, to attain the flow rate at the discharge of 1 m³/s

Taking pipe diameter as 15 inches = 0.381 m, the cross section area of pipe =

For required flow rate of 1 m³/s as per chosen pipe diameter, the flow velocity = (1 m³/s)/ (= 8.771m/s

Reynolds number =  =

Referring Chart

For pipe roughness (e/d) =0.001, e= 0.00038m or 0.38mm f = 0.02, and head loss for 50 m pipe length is computed using Darcy-Weishbach equations

 ,  = 131.6, head loss = 0.02*131.6*3.92 = 10.3 m for pipe roughness 0.38 mm

For cast iron pipe (e/d) =0.0005, e= 0.00019m or 0.19mm f= 0.017,

Head loss = 8.8 m for pipe roughness 0.19 mm or 190 micron

For cost iron pipe Surface roughness is 0.26 mm (From table 14.2)

For longer pipe of 300m length, let us chose pipe with roughness under 260 micron, then e/d = 0.00068, and f is 0.017

If we choose cost iron 50 m pipe also, Head loss = 0.017*131.6*3.92 m = 8.77 m

With same cost iron pipe for 300m long pipe, head loss = 0.017*(300/0.38)*3.92 m = 52.6 m.

The head loss in 300 m long pipe is quite large with cast iron pipe.

Loss can be minimized if we choose Smooth pipe. From the chart the f will get reduced from 0.017 to 0.0095

With smooth pipe for 300m long pipe, head loss = 0.0095*(300/0.38)*3.92 m = 29.4 m.

The head losses considered are the entrance loss, 90 deg bend elbow losses, losses at half opened gate valve, pipe friction losses, globe valve losses and exit loss.

Primary head losses (Includes all the pipes, glove valve, and gate valve) = 23.52+ 8.77+ 29.4+8.23+8.77= 78.69

Secondary head loss (Includes entrance, elbow bend, exit) = 1.92+1.02+1.02+4.1 = 8.06

Total head loss = 86.75

% of secondary head loss is close to 10%

Head loss due to component are taken from class notes

After solving energy equation we can conclude that, we require a pump of 1339 KW/ 1796 HP when 15 inch (0.381 m) dia pipe and elbows are used.

To lower the Pump power requirements, we need to increase the pipe diameter. Doubling the pipe diameter reduces flow velocity by factor of 4 and thus Head loss will reduce by factor of 16.

With 30 Inches pipe diameter

Taking pipe diameter as 30 inches = 0.762 m, the cross section area of pipe =

For required flow rate of 1 m³/s as per chosen pipe diameter, the flow velocity = 2.19/s

Reynolds number =  =

For cost iron pipe Surface roughness is 0.26 mm (From table 14.2)

For longer pipe of 300m length, let us chose pipe with roughness under 260 micron, then e/d = 0.00034, and f is 0.017

With same cost iron pipe for 300m long pipe, head loss = 1.63 m

Total head loss will reduce by a factor of 32

Final design    

Case 1:- By taking 300m Cast Iron Pipe

Case 2:- Taking 300m Smooth pipe

1. Summary

1. Component List

1. Head Losses

1. Appendix

Formulae:

For all head losses:        

                        h_L = K_L*((1/2g)*v²)

                        Where, h_L= Head loss, m

                                     K_L= Loss factor,

                                     g= Acceleration due to gravity= 9.81 m/s²,

                                     v= Flow velocity, m/s

1. For Entrance Loss,

K_L= 0.5.

1. For Globe Valve,

K_L= 6; Ref: Fluid Mechanics by Frank M. White. (Table 6.5)

• Pipe Friction Loss:

h_f = f (L/d) (v²/2g).

Where, h_f = Head loss in m due to Pipe Friction Loss                     

 f= Friction factor; Friction factor depends on a) Pipe roughness b) Pipe diameter c) Flow velocity

      Value taken from Ref: Fluid Mechanics by FM White (Equation 6.48)

      L= Length of Pipe;

      d= Diameter of Pipe;

                        g= Acceleration due to gravity= 9.81 m/s²,

                         v= Flow velocity, in m/s

1. Elbow 90^o Bend:

K_L= 0.26.

1. Gate Valve:

K_L= 2.1; from lecture notes.

1. Energy Equation:

The Mechanical Energy Equation in Terms of Energy per Unit Mass

The mechanical energy equation for a pump or a fan can be written in terms of energy per unit mass where the energy into the system equals the energy out of the system.

Epressure,in + Evelocity,in + Eelevation,in + Eshaft = Epressure,out + Evelocity,out + Eelevation,out + Eloss                                     

              (1)

Where,

p = static pressure (Pa, (N/m²))

ρ = density (kg/m³)

v = flow velocity (m/s)

g = acceleration of gravity (9.81 m/s²

hin= elevation height at inlet (m)

hout= elevation height at outlet (m)

E_shaft= net shaft energy per unit mass for a pump, fan or similar (J/kg)

E_loss = hydraulic loss through the pump or fan (J/kg)

The energy equation is often used for incompressible flow problems and is called the Mechanical Energy Equation or the Extended Bernoulli Equation.

Efficiency

According to (1) more loss requires more shaft work to be done for the same rise of output energy. The efficiency of a pump or fan process can be expressed as:

*The Mechanical Energy Equation in Terms of Energy per Unit Volume

The mechanical energy equation for a pump or fan (1) can also be written in terms of energy per unit volume by multiplying (1) with the fluid density – ρ:

  (2)

Where,

γ = ρ g =specific weight   (N/m3)

The dimensions of equation (2) are

Energy per unit volume

The Mechanical Energy Equation in Terms of Energy per Unit Weight involving Heads

The mechanical energy equation for a pump or a fan (1) can also be written in terms of energy per unit weight by dividing with gravity – g:

                          (3)

 = net shaft energy head per unit mass for a pump, fan in (m)

= loss head due to friction (m)

The dimensions of equation (3) are energy per unit weight (Nm/N = m)

E shaft = shaft power (W)

m = mass flow rate (kg/s)

Q = volume flow rate (m3/s)

1. Actual Calculations:

To attain discharge Flow Rate               Q= 1 m3/s discharge,  

Assume Diameter of Pipe/ Valve                       d= 0.381 m (15 inch);

Velocity of Fluid                                               v= Q/ (pi*d²/4)

                                                                        v= 1/ (3.14*0.381²/4)

                                                                        v= 8.77 m/s

Reservoir to Pipe: Entrance loss                   h_e=

                                                                           = =1.96 m

Globe valve head loss: Globe valve is fully open

                                                                        h_L= ===23.52 m

1. Pipe Friction Loss:

Length L= 50 m

Reynolds No. = (rho*v*d/ Dynamic Viscosity (µ)) = (998*8.77*0.381/0.001 Pa-s) =3335152

• Implies the flow is turbulent.

                              àPipe Material= Cast Iron à Roughness = 0.26

As per FM White Moody Chart,

                  f= 0.017

                                    h_f = f(L/d)(v²/2g)

                                        = 0.017* (50/0.381)(8.77²/2*9.81)=8.8 m

2. 90^o Elbow Bend 1 Loss:

h_L=0.2==1.0 m

3. Pipe Friction Loss:

Length L= 300 m

Reynolds No. = (rho*v*d/ Dynamic Viscosity (µ)) = (998*8.77*0.381/0.001 Pa-s) =3335152

• Implies the flow is turbulent.

                              àPipe Material= Cast Iron à Roughness = 0.26

As per FM White Moody Chart,

                  f= 0.017

                                    h_f = *  =  *

                                        = 52.6 m ( With cast iron pipe)

With doubling of pipe diameter to 30”, Velocity gets reduced to 2.19m/s, Re Number 0.9 Million and head loss gets reduced to

                                    h_f = *  =  *

                                        = 1.63 m

( With cast iron pipe), quite low so we do not need to go for smooth pipe.

4. Gate valve head loss: Gate valve is half closed

h_L= 2.1*((1/2g)*v²) = = 8.23 m

5. 90^o Elbow Bend 2 Loss:

h_L= 0.26*((1/2g)*v²) = 0.26* ((1/2*9.81)*(8.77) =1.019 m

6. Pipe Friction Loss:

Length L= 50 m

Reynolds No.= (rho*v*d/ Dynamic Viscosity(µ))= (998*8.77*0.381/0.001 Pa-s)  =3335152

• Implies the flow is turbulent.

                  àPipe Material= Cast Iron à Roughness = 0.26

As per FM White Moody Chart,

                  f= 0.017

                                    h_f = f(L/d)(v²/2g)

                                        = 0.017* (50/0.381)(8.77²/2*9.81) = 8.8 m

7. Pipe to tank :Exit loss

h_L= = = 4.1 m

114. Sum of head loss= 114.20 m
115. Gain of Elevation (Given) = 50 m

• Pump Head, h _shaft/pump = Sum of Head Loss + Gain of Elevation

                  = 86.75 + 50

                  =136.75 m

1. Pump Efficiency, ɳ = 0.8
2. Pump Power = =

                                                =1,338,834 watt = 1339 KWatt

In HP                                       = 1339 * 1.341 = 1796 HP

• Reference

1. Fluid mechanics FM White Book.
2. https://www.engineeringtoolbox.com/mechanical-energy-equation-d_614.html