Pipe Sizer: design explained. . .   

Pipe Sizer employs 2 options for pipe friction loss calculations, i.e., Hazen-Williams equation with valve & fittings Le method, or  Darcy-Weisbach equation with valve & fittings K method. Darcy-Weisbach method is generally considered more accurate than Hazen-Williams method. However, Hazen-Williams method is very popular since its friction coefficient, C, is not a function of velocity or pipe diameter. It is to note that Hazen-Williams equation is only valid for water at temperature 4 - 25 oC (40 -75 oF). 

You can choose water density and pipe materials with built-in database.  

Darcy friction factor, f, is solved by  Serghide's explicit equation - an approximation of the implicit Colebrook-White equation. Serghide's solution closely mirrors Colebrook's implicit solution within 0.0031%. 

Note: aPipeSizer can calculate minor (valve and fittings) loss using Le method or K method.

For multiple pipes friction losses, see   multiple Pipes Pressure Drop (mPPD) using Hazen-Willaims and Darcy-Weisbach equations with Equivalent Length (Le) and Resistance Coefficient (K) methods. 

Pipe Sizing based on Allowable Head Loss Method 

In some codes or design requirements, a recommended maximum allowable head loss (pressure drop) is specified. Generally speaking, an acceptable head loss (pressure drop) per 100 ft is around 2 to 5 psi (4.61 to 11.53 ft) to avoid excessive pipe pressure loss.

Note: ft/100ft = m/100m

Worked Example - Sizing by allowable Head Loss (in IP units) 

A copper pipe is used to deliver 20 gpm of water at ordinary temperature with a maximum allowed pressure drop of 5 psi/100 ft (11.53 ft/100 ft). What is the recommended pipe size that can be used?

Answer:

Flowrate, Q = 20 USgpm

Diameter, D = 1.5 in

Velocity, V = 3.63 ft/s

Worked Example - Friction loss by Darcy formula (in IP units) 

A 16-in diameter ductile iron cement-lined pipe carries city water at a flow rate of 8 ft3/s. What is the pipe friction loss through a pipe length of 100 ft? Assume the city water at 50 oF for density and dynamic viscosity.

Solutions:

Flowrate, Q = 8 ft3/s

Diameter, D = 16 in

Velocity, V = 5.7 ft/s

Friction loss by Darcy equation and K method ....

Pipe length, L = 100 ft

Valve and Fitting, K = 0

Water Density = 62.428 lb/ft3

Dynamic viscosity = 1.306 cP

Pipe roughness = 0.0001 ft

Reynolds Number = 543456

Friction Factor = 0.013993

Friction loss = 0.5356 ft H2O

HVAC Water formula: Cooling or Heating Water. . . 

The cooling or heating water flowrate-capacity-dT calculation is based on the following formula:

              q = Q x rho x Cp x dT

  where  q = heat rejection rate or heat load, kW

                 Q = water flowrate, m3/s

             rho = density of water, kg/m3

              Cp = specific heat, kJ/kg.K

               dT = temperature difference, oC

Did you know. . . Heat Rejection Factor (HRF) 

Conventionally, condenser water flowrate for water-cooled chiller is calculated as 3 USgpm/ton. This is equivalent to Heat Rejection Factor (HRF) of 1.25. With more efficient chillers being produced, the Heat Rejection Factor is lower than convention. In the absence of actual heat of compression of compressor, the following approximations may be used for design purpose:

0.8 kW/ton chiller: HRF = 1.25

0.7 kW/ton chiller: HRF = 1.22

0.6 kW/ton chiller: HRF = 1.19

0.5 kW/ton chiller: HRF = 1.16

0.4 kW/ton chiller: HRF = 1.14 

Note: the above approximations are only applicable for vapor compression chiller. Absorption chiller has much higher HRF.

Simply put, if you know the compressor kW from chiller selection data, the Total Heat Rejection (THR) is

THR (kW) = chiller cooling capacity (kW) + compressor kW power

HRF = THR / chiller cooling capacity

Note: 1 kW power is the equivalent of 1 kW refrigerant cooling load.

Worked Example (in IP units) 

Design/size the chilled-water and condenser water flowrate for a water-cooled chiller of capacity 340 tons.

Step 1: Calculate chilled-water flow rate

Water temperature @ 50 oF

Density = 62.428 lb/ft3

Specific heat = 1.002 btu/ibm.F

Chiller Capacity = 340 Ton

dT = 10 oF

Flowrate = 813.58 USgpm

Step 2: Chilled-Water Pipe Sizing Calculation

Flow rate = 813.58 USgpm

Pipe diameter = 6 in.

Pipe velocity = 9.2 ft/s (velocity too high!!!)

Frictional loss by Darcy equation....

Pipe length = 100 ft.

Water Density = 62.428 ib/ft3 (Water @ 50 oF)

Dynamic viscosity = 1.306 cP

Reynolds number = 328356

friction factor = 0.016832

Friction loss = 4.4600 ft H2O (friction loss rate per 100ft is too high?? Expected as the pipe velocity is beyond the norm. Calculate again..... as easy as 1,2,3 with aPipeSizer.)

Step 3: Calculate Condenser water flowrate

Water temperature @ 86 oF

Density = 62.178 lb/ft3

Specific heat = 0.998 btu/ibm.F

Chiller Capacity = 340 Ton

Heat rejection factor = 1.25 (in the absence of known heat of compression of compressor)

Total heat rejection = 425.00 Ton

dT = 10 oF

Flowrate = 1024.48 USgpm