Step-by-Step Guide: Pump Hydraulic Calculation for Concentrated Sulfuric Acid
Problem Statement
98 % Sulfuric Acid is stored in atmospheric storage tank in tank farm area of a plant, which is to be pumped by a centrifugal pump to a reactor located in process area at a rate of 91300 kg/hr. Maximum allowable velocity in suction line is 0.8 m/s and maximum allowable velocity in discharge line is 1.8 m/s. Calculate pump differential head, NPSH, pump power and pump shut off pressure. Consider efficiency of pump as 70 %.
Solution:
Process Data:
Operating Temperature: 30oC,
Density: 1826 kg/m3,
Viscosity: 15cP
Design Flow rate: 91300/1826 = 50 m3/hr,
Vapor Pressure: 0.0000014 bar.
Tank Parameters and Elevations.
Tank Details: Tank elevation above ground: 0.8 m,
Tank operation pressure: 0 barg, operating temperature: 30 oC,
Vapor pressure: 0.0000014 bar,
Design pressure: 0.17 barg,
Tank dimensions: 9 m Height X 9 m Diameter,
HHLL: 8 m, LLLL above pump suction nozzle: 0.3 m, Pump suction nozzle elevation
above bottom of tank: 0.3 m.
Reactor Details: Reactor elevation above ground: 8m,
Pump inlet nozzle elevation above bottom tangent line of vessel: 6 m,
Pump centerline elevation above ground: 0.7 m,
Operating pressure of reactor: 4 barg.
Pump Suction side fittings: Pipe material is carbon steel.
Pipe length: 7 m,
Strainer: 1 Nos having L/D = 250,
Full bore ball valve: 2 Nos having L/D = 3,
90o Elbow: 3 Nos having L/D = 30.
Pump discharge side fittings: Pipe material is carbon steel.
Pipe length: 250 m,
Full bore ball valve: 4 Nos having L/D = 3,
90o Elbow: 10 Nos having L/D = 30,
Control Valve: 1 Nos having pressure drop of 0.7 bar at max flow,
Flow transmitter having pressure drop of 0.2 bar.
Calculation:
Suction Side:
Volumetric flow = 50/3600 = 0.0139 m3/s
Velocity: This is trial and error step. By multiple iterations 6" SCH 40 size having ID of 154.08 mm will suffice maximum velocity condition.
Reynolds No:
Re>4100, flow is turbulent. So, we can use Colebrook-White equation for smooth pipe for friction factor.
By solving this equation, we will get value of f as 0.00716.
To find Pressure drop of pipe, Darcy-Weisbach equation is used.
To find pressure drop of fitting equivalent length method is used.
Equivalent length of fitting = {(1*250) +(2*3) +(3*30)} * 0.15408 = 53.3 m
Total equivalent length = 53.3 + 7 = 60.3 m.
Static pressure gains due to elevation difference between pump and tank.
Static head gain due to elevation difference between tank low low liquid level and pump centerline,
Conversion of static head to pressure,
Now, Pump Suction pressure is suction vessel operating pressure plus pressure gain due to static head minus the pressure loss due to friction,
Now, NPSHa is absolute suction pressure minus the vapor pressure,
Discharge Side:
Volumetric flow = 50/3600 = 0.0139 m3/s
Velocity: This is trial and error step. By multiple iterations 4"SCH 40 size having ID of 102.26 mm will suffice maximum velocity condition.
Reynolds No:
Re > 4100, flow is turbulent. So, we can use Colebrook-White equation for smooth pipe for friction factor.
By solving this equation, we will get value of f as 0.00646.
To find Pressure drop of pipe, Darcy-Weisbach equation is used.
To find pressure drop of fitting equivalent length method is used.
Equivalent length of fitting = {(4*3) +(10*30)} * 0.10226 = 31.9 m.
Total equivalent length = 31.9 + 250 = 281.9 m
The discharge line contains two pieces of inline equipment, one is control valve having pressure drop of 0.7 bar at maximum flow and second is flow transmitter having pressure of 0.2 at maximum flow.
Static pressure loss due to elevation difference between pump and reactor.
Static head loss due to elevation difference between pump centerline and pump in nozzle of reactor,
Conversion of static head to pressure,
Now, Pump discharge pressure is reactor operating pressure plus pressure loss due to static head plus the pressure loss due to friction,
Now we need to find power required by pump to perform task, below formula is used to find power consumption by the pump,
Now last part is pump shut off pressure. For centrifugal pump shut off pressure is the pressure at the discharge nozzle where there is no flow (zero flow). We can estimate pump shut off pressure using below formula,
Maximum suction pressure is the sum of design pressure of suction vessel (set pressure of pressure safety device) plus the maximum pressure gain due to liquid height (i.e. from HHLL). For this case maximum suction pressure is calculated as follows,
Now we have to find the differential shut off pressure of pump, only the pump manufacturer can tell the actual differential shut off pressure of the selected pump model. But as a rule of thumb, we can estimate differential shut off pressure as 1.25 times the differential pressure.
Final Results:
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