Pressure drop in pipe

Calculate pressure drop in straight cylidrical steel pipe of district heating system (where water is a heat carrier) that is a result of pipe orientation in space (hydrostatic component), and friction between water and internal wall of pipe.

Usage

dropp(
  temperature = 130,
  pressure = mpa_kgf(6),
  flow_rate = 1276,
  d = 1,
  len = 1,
  roughness = 0.006,
  inlet = 0,
  outlet = 0,
  method = "romeo"
)

Arguments

temperature: temperature of heat carrier (water) inside the pipe, [°C]. Type: assert_double.
pressure: absolute pressure of heat carrier (water) measured at the entrance (inlet) of pipe, [MPa]. Type: assert_double.
flow_rate: amount of heat carrier (water) that is transferred by pipe during a period, [ton/hour]. Type: assert_double.
d: internal diameter of pipe, [m]. Type: assert_double.
len: pipe length, [m]. Type: assert_double.
roughness: roughness of internal wall of pipe, [m]. Type: assert_double.
inlet: elevation of pipe inlet, [m]. Type: assert_double.
outlet: elevation of pipe outlet, [m]. Type: assert_double.
method: method of determining Darcy friction factor. Type: assert_choice. (see Details)

Value

pressure drop at the outlet of pipe, [MPa]. Type: assert_double.

Details

The underlying engineering model for calculation of pressure drop considers only two contributions (components):

Pressure drop due to gravity (hydrostatic component).
Pressure drop due to friction.

The model does not consider any size changes of pipe and presence of fittings.

For the first component that depends on pipe position in space the next figure illustrates adopted disposition of pipe.

So, the expression for the first component can be written as:

$$g \rho (outlet - inlet)$$

where g - is gravity factor, $m/s^2$, and $\rho$ - density of water (heat carrier), $kg/m^3$; inlet and outlet are appropriate pipe elevations (under sea or any other adopted level), $m$.

The second component comes from Darcy–Weisbach equation and is calculated using heating carrier regime parameters (temperature, pressure, flow_rate). Temperature and pressure values of heat carrier define water properties according to IAPWS formulation.

Several methods for calculating of Darcy friction factor are possible and limited to the next direct approximations of Colebrook equation:

romeo: Romeo, Royo and Monzon, 2002
vatankhan: Vatankhan and Kouchakzadeh, 2009
buzelli: Buzzelli, 2008

According to Brkic, 2011 approximations errors of those methods do not exceed 0.15 % for the most combinations of Reynolds numbers and actual values of internal wall roughness of pipe.

References

W.Wagner et al. The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, J. Eng. Gas Turbines Power. Jan 2000, 122(1): 150-184 (35 pages)
M.L.Huber et al.New International Formulation for the Viscosity of $H_2O$, Journal of Physical and Chemical Reference Data 38, 101 (2009);
D.Brkic. Journal of Petroleum Science and Engineering, Vol. 77, Issue 1, April 2011, Pages 34-48.
Romeo, E., Royo, C., Monzon, A., 2002. Improved explicit equation for estimation of friction factor in rough and smooth pipes. Chem. Eng. J. 86 (3), 369–374.
Vatankhah, A.R., Kouchakzadeh, S., 2009. Discussion: Exact equations for pipeflow problems, by P.K. Swamee and P.N. Rathie. J. Hydraul. Res. IAHR 47 (7), 537–538.
Buzzelli, D., 2008. Calculating friction in one step. Mach. Des. 80 (12), 54–55.

Examples

 library(pipenostics)

# Typical pressure drop for horizontal pipeline segments
# in high-way heating network in Novosibirsk
dropp(len = c(200, 300))
#> [1] 0.0007000666 0.0010500999

#[1] 0.0007000666 0.0010500999