Hydraulic Calculations

the following equations are used to perform hydraulic calculations in optioneer bernoulli equation p 1+\frac{1}{2}\rho v {1}^2+\rho gh {1}=p 2+\frac{1}{2}\rho v {2}^2+\rho gh {2} which can be written re written as h {1}+\frac{p {1}}{\rho g}+\frac{v {1}^2}{2g} l {friction}=h {2}+\frac{p {2}}{\rho g}+\frac{v {2}^2}{2g} where h 1, p 1, and v 1 are the height, pressure and velocity at the start of the segment being calculated and h2, p 2 and v 2 are height, pressure and velocity at the end of the segment ρ is the fluid's density and g is the acceleration due to gravity friction losses friction losses are considered along the pipeline length using the darcy weisbach equation the friction loss is meters of head loss and is expressed as l {friction}=f \frac{l}{d} \frac{v^2}{2g} where f is the friction factor of the pipe, l is the total length of the option , d is the inner diameter of the pipe, v is the mean flow velocity, and g is the acceleration of gravity the friction factor f is calculated using the swanee jain equation f=\frac{0 25}{\left \[ log\left\\{\frac{\varepsilon }{3 7d}+\frac{5 74}{re^{0 9}} \right\\} \right ]^2} where e is the absolute roughness of the pipe, d is the inner diameter of the pipe and re is reynolds number total pump energy the total pump energy (shaft power) required in a system is calculated based on the total required head to overcome any negative pressure in the option this is based off the hydraulic gradient, including friction losses p {s}(kw)=(\frac{\frac{qh\rho 9 81}{eff {pump}eff {motor}}}{3 610^6}) 1 1 where q is the mean flow rate, h is your total required pumping head in meters, ρ is the fluid's density a nd eff pump and motor is the efficiency of each component hydraulic head hydraulic head represents the mechanical energy in the system where by its defined by the pressure head in addition to the elevation head of the system h= \frac{p}{\rho g}+\frac{v^{2}}{2g}+z velocity the velocity is a variable that is assumed to be the relationship between the mean flow velocity and the volumetric flow and is calculated in the following way q=av where q is the volumetric flow rate which within optioneer is an input parameter labeled as mass flow rate, and a is cross sectional wetted area using there two metrics optioneer calculates v , our mean flow velocity h= \frac{p}{\rho g}+\frac{v^{2}}{2g}+z opex pump operation costs the operational cost of the pumps in the system can be calculated by the total required shaft power in the system by the total running time opex {pumpannual}= p {s}(kw) {hr} hr {perday} 365 p {cost1} where by p s( kw)hr is your total shaft power of the pumps per hour , hr per day is the pump run time per day, and pcost1 is your cost of electricity per kw lifetime pump operation cost the lifetime pump operation costs is calculated in the following way opex pumplifetime = opex pump annual pump {years} w here by pump years is the expected life span of the pump in years