Introduction

Very frequently, we need to calculate frictional pressure drops in pipelines. Many of us may have domestic pumps in our households. After we estimate the pump flow from expected consumption of water, we need to calculate the pump head for purchasing a suitable pump. The following is an example of calculation of pressure drop when the flow and pipe geomerty is known.

Input Data(assumed)

1. Pipe flow -10 m³/h

2. Fluid-Water at 25⁰C. 

3. Pipe material-commercial galvanised carbon steel (absolute roughness ε=0.15 mm)

4.. Flow geometry as below(total pipe length L=20 m).

h₁=3m

h₂=12m

Calculation

Step-1 Calculation of flow velocity

From pipe dimension table for 25mm NB std thickness pipe

OD (D)=33.4 mm

Thickness (t)=3.38 mm

Hence ID(d)=D-2t=33.4-2x3.38=26.64 mm=0.02664 m

Pipe flow area (A)=(π/4)d²= (π/4)x0.02664²=0.000557 m² 

Pipe flow (Q)=10 m³/h=10/3600=0.00278 m³/s

Hence pipe flow velocity(V)=Q/A=0.00278/0.000557=4.98 m/s

Step-2 Calculation of Darcy's Friction Factor(f)

Kinematic viscosity of water(ν)=8.92x10^-7 m²/s

Reynold's number (Re)=Vd/ν=4.98x0.02664/8.92x10^-7=1.9x10⁵

Re>2000 hence flow is turbulent

For determining f we use Moody's chart s below:

 ^{Relative roughness (ε/d)=0.15/1000/0.02664=0.005631}

^{We noe find f from Re and ε/d as follows}

^{Hence f=0.031}

 ^{Step 3 Calculation Pipe Friction Drop}

 Total pipe length L=20 m

Minor losses

Minor losses are calculated by K factors. Different K factors are available in the internet(refer Crane Technical Paper 410)

a) Inlet loss-K₁=1

b) Foot valve with strainer-pressure drop Δp_f1=0.1 bar(assumed)=1x10⁴ Pa

c) Elbows 90⁰ -3 Nos, K₂=3x30f=3x30x0.031=2.79

d) Gate valve -2 nos, K3=2x8f=2x8x0.031=0.496

e) Exit loss, K4=1

Total head drop

h_f= (fL/D+K₁+K₂+K₃+K₄)V²/2g+ Δp_f1/ρg (Note :ρ=density=1000 kg/m³)

=(0.031x20/0.02664+1+2.79+0.496+1)(4.98²/2x9.81)+1x10⁴/(1000x9.81)

=37.12 mwc

Step 4 Calculation of Pump Head

In addition to frictional head loss we have static head increase

Pump head (H)=(h₁+h₂)+h_f= 3+12+37.12

H=52.12 mwc

We normally take some margin (say 15 %)for future increase in pipe friction drop due to ageing and calculation uncertainties.

So

H=52.12x1,15=60 mwc

Pump details, 10 m³/h flow, 60 mwc head.