PUMP EQUATIONS
Pump Energy Consumption
The energy consumption of the pumps depends on two factors:
Pump BHP = GPM x TDH x SG / (3960 x Efficiency)
Pump BHP = GPM x PSI x SG / (1713 x Efficienc y)
Where
• BHP = brake horse power
• Q = water flow, gallons per minute (GPM)
• TDH = Total Dynamic Head, ft
• SG = Specific Gravity, for water it is 1
• Efficiency = Pump efficiency from its pump curves for the water flow and TDH
Power consumption, KWH = KW input x operating hours
The KW input will depend on the motor efficiency and pump power requirement. (1 KW = 0.746 HP)
Pump Motor Horsepower
Motor HP = BHP / Motor Ef f
Where
• BHP = Break Horsepower
• Motor Ef f = Motor drive efficiency usually 80-95%
Pump Affinity Laws
Effect on centrifugal pumps of change of speed or impeller diameter
Capacity varies directly as the speed or impeller diameter (GPM x rpm x D)
Head varies as the square of speed or impeller diameter (GPM x rpm2 x D2)
BHP varies as the cube of the speed or impeller diameter (BHP x rpm3 x D3)
Specific Gravity
Specific gravity is direct ratio of any liquid’s weight to the weight of water at 62 deg F. Water at 62 deg F weighs 8.33 lbs per gallon and is designated as 1.0 specific gravity. By definition, the specific gravity of a fluid is: SG = PF / PW
Where PF is the fluid density and PW is water density at standard conditions.
Example Specific Gravity of HCl = Weight of HCl / Weight of Water = 10.0 / 8.34 = 1.2
Head and Pressure
To start, head is not equivalent to pressure. Since the pump is a dynamic device, it is convenient to consider the head generated rather than the pressure. The term “Head” is usually expressed in feet whereas pressure is usually expressed in pounds per square inch. The relations hip between two is
PSI = Head (feet) x Specific Gravity / 2.31
Velocity Head
VH = V2 /2g
Where
• VH = Velocity head in ft
• V = Velocity in ft/s
• g = Acceleration due to gravity (32.17 ft/s2 )
Bernoulli's equation
The pump generates the same head of liquid whatever the density of the liquid being pumped. In the following equation (Bernoulli's equation) each of the terms is a head term: elevation head h, pressure head p and v elocity head v2 /2g. Head is equal to specific energy, of which the units are lbf-ft/lbf. Therefore, the elevation head is actually the specific potential energy, the pressure head, the
specific pressure energy and the velocity head is the specific kinetic energy (specific means per unit weight).
h + p/y + v2 /2g = E = Constant
Where
• h: elevation in ft;
• p: pres sure lb/sq-in;
• y: fluid specific weight
• v: velocity in ft/s
• g: acceleration due to gravity (32.17 ft/s2);
• E: specific energy or energy per unit mass.
Note: A centrifugal pump develops head not pressure. All pressure figures should be converted to feet of head taking into considerations the specific gravity.
Pump NPSH
To determine the NPSH available, the following formula may be used
NPSHA = HA ± HS - HF - HVP
Where
• NPSHA = Net Positive Suction Available at Pump expressed in feet of fluid
• NPSHR = Net Positive Suction Required at Pump (Feet)
• HA = Absolute pressure on the surface of the liquid where the pump takes suction, expressed in feet. This could be atmospheric pressure or vessel pressure (pressurized tank). It is a positive factor (34 Feet for Water at Atmospheric Pressure)
• HS =Static elevation of the liquid above or below the centerline of the impeller, expressed in feet. Static suction head is positive factor while static suction lift is a negative factor.
• HF = Friction and velocity head loss in the piping, also expressed in feet. It is a negative factor.
• HVP = Absolute vapor pressure of the fluid at the pumping temperature, expressed in feet of liquid. It is a negative pressure.
The Net Positive Suction Head (N.P.S.H.) is the pressure head at the suction flange of the pump less the vapour pressure converted to fluid column height of the fluid. The N.P.S.H. is always positive since it is expressed in terms of absolute fluid column height. The value, by which the pressure in the pump suction exceeds the liquid vapour pressure and is expressed as a head of liquid and referred to as Net Positive Suction Head Available – (NPSHA). This is a characteristic of the suction system design. The value of NPSH needed at the pump suction to prevent the pump from cavitating is known as NPSH Required – (NPSHR). This is a characteristic of the pump design.
Note that NPSHA > NPSHR i.e. the N.P.S.H. available must always be greater than the N.P.S.H. required for the pump to operate properly.
Pump Specific Speed
Equation below gives the value for the pump specific speed;
Ns = (Nr x Q) / (H)3/4
Where
• Ns = Specific speed
• Q = Flow in US gallons per minute (GPM)
• Nr = Pump speed, RPM
• H = Head, ft
Specific speed is a dimensionless quantity. Specific speed is indicative of the shape and characteristics of an impeller. Impeller form and proportions vary with specific speed but not the size. It can be seen that there is a gradual change
in the profiles from radial to axial flow configuration. Studies indicate that a pump efficiency at the best efficiency point (BEP) depends mainly on the specific speed, and a pump with specific speed of 1500 is more efficient then the one with specific speed of 1000
The energy consumption of the pumps depends on two factors:
Pump BHP = GPM x TDH x SG / (3960 x Efficiency)
Pump BHP = GPM x PSI x SG / (1713 x Efficienc y)
Where
• BHP = brake horse power
• Q = water flow, gallons per minute (GPM)
• TDH = Total Dynamic Head, ft
• SG = Specific Gravity, for water it is 1
• Efficiency = Pump efficiency from its pump curves for the water flow and TDH
Power consumption, KWH = KW input x operating hours
The KW input will depend on the motor efficiency and pump power requirement. (1 KW = 0.746 HP)
Pump Motor Horsepower
Motor HP = BHP / Motor Ef f
Where
• BHP = Break Horsepower
• Motor Ef f = Motor drive efficiency usually 80-95%
Pump Affinity Laws
Effect on centrifugal pumps of change of speed or impeller diameter
Capacity varies directly as the speed or impeller diameter (GPM x rpm x D)
Head varies as the square of speed or impeller diameter (GPM x rpm2 x D2)
BHP varies as the cube of the speed or impeller diameter (BHP x rpm3 x D3)
Specific Gravity
Specific gravity is direct ratio of any liquid’s weight to the weight of water at 62 deg F. Water at 62 deg F weighs 8.33 lbs per gallon and is designated as 1.0 specific gravity. By definition, the specific gravity of a fluid is: SG = PF / PW
Where PF is the fluid density and PW is water density at standard conditions.
Example Specific Gravity of HCl = Weight of HCl / Weight of Water = 10.0 / 8.34 = 1.2
Head and Pressure
To start, head is not equivalent to pressure. Since the pump is a dynamic device, it is convenient to consider the head generated rather than the pressure. The term “Head” is usually expressed in feet whereas pressure is usually expressed in pounds per square inch. The relations hip between two is
PSI = Head (feet) x Specific Gravity / 2.31
Velocity Head
VH = V2 /2g
Where
• VH = Velocity head in ft
• V = Velocity in ft/s
• g = Acceleration due to gravity (32.17 ft/s2 )
Bernoulli's equation
The pump generates the same head of liquid whatever the density of the liquid being pumped. In the following equation (Bernoulli's equation) each of the terms is a head term: elevation head h, pressure head p and v elocity head v2 /2g. Head is equal to specific energy, of which the units are lbf-ft/lbf. Therefore, the elevation head is actually the specific potential energy, the pressure head, the
specific pressure energy and the velocity head is the specific kinetic energy (specific means per unit weight).
h + p/y + v2 /2g = E = Constant
Where
• h: elevation in ft;
• p: pres sure lb/sq-in;
• y: fluid specific weight
• v: velocity in ft/s
• g: acceleration due to gravity (32.17 ft/s2);
• E: specific energy or energy per unit mass.
Note: A centrifugal pump develops head not pressure. All pressure figures should be converted to feet of head taking into considerations the specific gravity.
Pump NPSH
To determine the NPSH available, the following formula may be used
NPSHA = HA ± HS - HF - HVP
Where
• NPSHA = Net Positive Suction Available at Pump expressed in feet of fluid
• NPSHR = Net Positive Suction Required at Pump (Feet)
• HA = Absolute pressure on the surface of the liquid where the pump takes suction, expressed in feet. This could be atmospheric pressure or vessel pressure (pressurized tank). It is a positive factor (34 Feet for Water at Atmospheric Pressure)
• HS =Static elevation of the liquid above or below the centerline of the impeller, expressed in feet. Static suction head is positive factor while static suction lift is a negative factor.
• HF = Friction and velocity head loss in the piping, also expressed in feet. It is a negative factor.
• HVP = Absolute vapor pressure of the fluid at the pumping temperature, expressed in feet of liquid. It is a negative pressure.
The Net Positive Suction Head (N.P.S.H.) is the pressure head at the suction flange of the pump less the vapour pressure converted to fluid column height of the fluid. The N.P.S.H. is always positive since it is expressed in terms of absolute fluid column height. The value, by which the pressure in the pump suction exceeds the liquid vapour pressure and is expressed as a head of liquid and referred to as Net Positive Suction Head Available – (NPSHA). This is a characteristic of the suction system design. The value of NPSH needed at the pump suction to prevent the pump from cavitating is known as NPSH Required – (NPSHR). This is a characteristic of the pump design.
Note that NPSHA > NPSHR i.e. the N.P.S.H. available must always be greater than the N.P.S.H. required for the pump to operate properly.
Pump Specific Speed
Equation below gives the value for the pump specific speed;
Ns = (Nr x Q) / (H)3/4
Where
• Ns = Specific speed
• Q = Flow in US gallons per minute (GPM)
• Nr = Pump speed, RPM
• H = Head, ft
Specific speed is a dimensionless quantity. Specific speed is indicative of the shape and characteristics of an impeller. Impeller form and proportions vary with specific speed but not the size. It can be seen that there is a gradual change
in the profiles from radial to axial flow configuration. Studies indicate that a pump efficiency at the best efficiency point (BEP) depends mainly on the specific speed, and a pump with specific speed of 1500 is more efficient then the one with specific speed of 1000
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