Pump And Hydraulic Calculation

Pump and Hydraulic Calculation Total Static Head (h, m) is different elevation between suction head and delivery head.

h = hd ± hs

η hyd =

hm h

Overall Efficiency (ηo) is the ration of theory power with actual power.

ηo =

Ptheory Pactual

=

γQh m P

Where γ =Specific Weight = gρ (N/m3) P = Drive power (W) Energy Equation (Bernouli’s Equation)

P1 V2 P V2 + Z 1 + 1 + h p − hL = 2 + Z 2 + 2 γ 2g γ 2g Suction Head (hs, m) is elevation different from minimum possibility of water surface level to center line of suction pump. (- when reference point higher than suction pump, + when reference point lower than suction pump) Discharge Head or Delivery Head (hd, m) is elevation different from maximum possibility of water surface level to center line of discharge pump. Absolute Static Head (h, m)

has =

Pas ( pa ) ρg

Net Head (hnet, m) is power in term of water height. Manometric Head (hm, m) is actual head which pump can create, by checking thought pressure gauge.

hm =

Pout − Pin ρg

Which, normally hm < h Hydraulic Power (HP, W) is the theory power for liquid transportation. HP = ρghQ

Where P1 = Pressure from 1st reference point (Pa) P2 = Pressure from 2nd reference point (Pa) Z1 = water level from 1st reference point (m) Z2 = water level from 2nd reference point (m) V1 = Decreasing velocity of 1st reference point (m/s) V2 = Increasing velocity of 2nd reference point (m/s) hP = Power receiving from pump (m) hL = Power lose from piping and fitting (m) (if either size of 1st reference or 2nd reference are larger than 10 times of pipe diameter, V1 and V2 can be negligible) Net Head (hnet, m) under Bernouli’s equation is the following.

V 2 V 2  P P  h p =  2 − 1  + ( Z 2 − Z1 ) +  2 − 1  + hL γ  γ  2g 2g  Net Positive Suction Pressure (NPSH) is the net suction pressure after minus suction loss and vapour pressure. NPSH consist of NPSHA and NPSHR

Where Q = Flow Rate (m3/s) Break Power or Shaft Power (BP, W) is power input to pump which related with pump efficiency (ηp)

BP =

HP

ηP

Drive Power (DP, W) is power input to motor drive which related with motor efficiency (ηD)

DP =

BP

ηD

Hydraulic Efficiency (ηhyd) or Manometric Efficiency (ηmano) is the ratio of actual head with theory head.

NPSHA (available net positive suction head, m) can be calculated from the actual location.

NPSH

A

=

P1 V2 P + ( Z 1 − Z 2 ) − 2 − hL − V γ 2g γ

Basis 1st reference point is bigger than suction pipe more than 10 times, V1 = 0 m/s and P2 must more than Pv to protect cavitation (P2 > Pv) then

P2

γ

= NPSH

A

+

PV

γ

Where Pv = Vapour Pressure (Pa) NPSHR (Required net positive suction head, m) this value will get from manufacture but, anyway, roughly a calculation for expedition pump characteristic is; NPSH

R

 N Q ( m 3 / min) =3   S 

Cavitation incase loss suction pump

4

   

Where N = revolution (rpm) S = Specific suction velocity

rpm × m 2 min

Recommendation NPSHA for pump selection.

NPSH

A

≥ 1.3 NPSH

R

From Bernouli’s equation

P1 V2 P V2 + Z 1 + 1 + h p − hL = 2 + Z 2 + 2 γ 2g γ 2g Assume that V1 = 0 m/s, Z1 = 0 m (reference point) and hp is not available. Then

Vs2 hs = − − − h fs γ γ 2g Patm

Cavitation is main problem about pump such as abnormal sound, vibration, corrosion and less performance. Cavitation can be occurred generally two styles, one is throatting in pipe and the other one is loss suction pump. Cavitation in pipe (throatting) From Bernouli’s equation

P1 V2 P V2 + Z 1 + 1 + h p − hL = 2 + Z 2 + 2 γ 2g γ 2g Assume that pipe is in same elevation then Z1 = Z2 Flow rate is constant but velocity is related with pipe size. And pressure which can cause cavitation is vapour pressure. From Pv = Patm + Pgauge which Pgauge = P2 Then P2 = PV − Patm

Pv

Where V2 = Vs = Suction velocity (m/s) hfs Suction Friction Loss (m) Note The result, hs is the theory maximum allowable height (deep) for suction pipe. The other method for checking the height (deep) and pump are suitable properly, or not, by checking Thoma cavitation coefficient (σ). Thoma Cavitation Coefficient (σ)

( Patm − PV ) σ=

V 2  − s γ  2 g + hs + h fs  hm

and Critical Thoma Cavitation Coefficient (σc)

 N  σ c = 0.103  S   1000 

4

3

Criteria Cavitation will happen when σ < σ c Friction loss (hL or hf, m) is loss from pipe length (main-loss) and any fitting (minor loss). Calculation method is found many formulas.

1- Equivalent pipe length and graph WilliamsHazen Using method graph Williams-Hazen. 11. Count all the fitting (ex. Valve, elbow, etc) 22. Mark the point on the graph, x-axial presented flow rate (m3/min) and y-axial present friction loss per 100 m. (hL)

1- Darcy-Weisbach Equation (Moody-Chart or Colebrook Equation or Haaland Equation) Using method Moody-Chart (for calculation mainloss) 11. Darcy-Weisbach Equation LV2 hf = f d 2g Where f= Friction factor which can be found from MoodyChart or Colebrook’s equation or Haaland’s equation. 12. Moody-Chart is presented the relation of Reynolds number (Re), Relative roughness (ε/d) and Friction factor. Where Re = Reynolds number =

ρVd vd or µ ν

ε = Pipe roughness (ft, mm) Where μ = Dynamic Viscosity (kg/m.s, N.s/m2) υ = Kinematics Viscosity =

1

µ (m2/s) ρ

about verify f-value by trial and error method.

94. Haaland’s Equation 10

 ε 1.11  1 6 . 9    = −1.8 log d  + 1  Re   3 .7  f 2   

Appling method of Moody-Chart (for calculation main-loss and minor-loss) 14. Darcy-Weisbach Equation will become 2 hf

 L N V 2 =  f + ∑ Ki   d i −1  2 g

Where Ki = minor-loss coefficient V = Velocity (m/s) Because of minor-loss head from N

h f ( min or ) = ∑ K i i =1

V2 2g

2Pipe roughness (ε, ft or mm) 3

4 K-Value can be checked from “Resistance coefficient chart” as attachment. Minimum Required Flowrate (MF, m3/hr) Min-flow is the required flow rate to pump for protection the liquid temperature increasing. (Assume temperature rises less than 15oC)

5

63. Colebrook’s equation  ε 1 2.51  + 7 1 = −2 log   3.7d Re f 1 2  f 2   8But the Colebrook’s equation has some difficulty

 m3 QMF = 2.10 ×10 −4 Q  hr 

  h(m) 

Which, normally, this value will be provided by manufacture.

Pump Specific Speed (Ns, dimensionless) Pump specific speed is used for impeller selection or estimate pump efficiency (%)

Ns =

(

N (rpm) Q l

)

min

h 0.75

Viscosity Correction, This method is applied for high viscosity pump which can be predicted by multiply correlation factor with water pump. Where QP' = Capacity of pump when use with water

hP' = Head of pump when use with water NPSH ' = NPSH of pump when use with water

ηP'

= Water pump Efficiency The correlation equations are following.

QP = CQ × QP' hP = C H × hP' NPSH = C H × NPSH

ηP = Cη ×ηP'

'

Piping, General recommendations for good design practice. 1- Branches of suction pipe This is kind of manifold, to protect the interference the following criteria should be considered.

Pump System consists of two type, parallel and series. 1- Parallel System QT QT

≠ Q +Q

≈

1

2

1.1Q1 (Depend on system loss)

11. Vm = Manifold velocity ≤ 0.6 0.9 m/s 22. Suction length (Ls) ≥ 10.Ds (suction diameter) 33. Vs = Suction Velocity ≤ 1.5 m/s

1- Suction sump WL = Water Level

1- Series System

The detail for calculation suction sump is presented by the other documents.

HT ≠ H1+H2 Sometime, total series flow more than parallel flow. It depends on system loss, mean downstream friction loss.

To safe the power consumption, adjusting revolution is the other choice except pipe loss reduction.

N Qn = Qo  n  No

  

N H n = H o  n  No N Pn = Po  n  No

  

  

2

3

Where Subscribe n = New and o = Old The other way to change pump performance is the cutting impeller. This method might use for reduce downstream pressure.

D Qn = Qo  2 n  D2 o

  

D H n = H o  2 n  D2 o D  Pn = Po  2 n   D2 o  Where D2 = Diameter of impeller (mm)

Conclusion to get the higher flow Big pipe (low hf) – Parallel is advantage. Small pipe (high hf) – Series is advantage. System Loss Equation This formula is provided for head-loss-curve presentation which can be applied for checking the following. 11. Performance curve, operation point 22. Estimate total flow of parallel or series system 3 1.85

h f =10 .666 ×130

−1.85

Q = Flow rate (m3/min) Affinity Law

×D

−4.87

Q  ×   60 

×L

3

  

2

End of doc.--