Pump Head Calculator

Total dynamic head is the energy per unit weight of fluid that a pump must add, expressed in feet of the fluid being pumped. Working in head rather than pressure is deliberate: a centrifugal impeller of a given diameter and speed produces a nearly constant head regardless of fluid density, so the same pump develops the same feet of head on water or on brine, while the pressure and the power both scale with specific gravity. TDH is assembled from four Bernoulli terms. Static head is the elevation difference between source and destination. Friction head covers pipe wall losses from the Darcy-Weisbach relation plus minor losses at elbows, valves and fittings, which in a compact piping arrangement can be 30 to 50 percent of the total. Velocity head is the kinetic term and is usually small. Pressure head converts any vessel pressure difference at 2.31 feet per psi for water. Sizing rules of thumb bound the inputs. Suction lines are normally kept at 4 to 8 feet per second and discharge lines at 6 to 12, with friction losses of about 1 to 4 feet per 100 feet of pipe considered economical; below 3 feet per second solids settle, and above 15 the losses, noise and erosion become severe. The Darcy friction factor for commercial pipe in turbulent flow generally falls between 0.015 and 0.03. Two limits matter. Pump efficiency of 50 to 85 percent applies only near the best efficiency point, so a pump run far from its design flow will not meet the calculated brake horsepower. And TDH says nothing about suction conditions: net positive suction head available must exceed the manufacturer required value by 2 to 3 feet or the pump cavitates regardless of how well the discharge side was calculated.

The friction term at the heart of any head calculation carries the names of two nineteenth century engineers. Julius Weisbach, a German professor of mechanics at the Freiberg mining academy, published in the 1840s the form of the equation in which head loss is proportional to a dimensionless factor times the length to diameter ratio times the velocity head. What he lacked was reliable data for that factor. Henry Darcy, the French engineer responsible for the water supply of Dijon, supplied it through careful pipe experiments reported in the 1850s, establishing that roughness of the pipe wall, not just its diameter, controlled the loss. Determining the friction factor remained laborious until the twentieth century. Colebrook and White published their implicit correlation covering the transition between smooth and fully rough turbulent flow in 1939, and in 1944 Lewis Ferry Moody plotted it as the chart engineers still call the Moody diagram, allowing a factor to be read from Reynolds number and relative roughness in seconds. Pump technology developed alongside: John Appold demonstrated a curved vane centrifugal pump at the Great Exhibition in London in 1851 that roughly tripled the efficiency of the straight vane designs of the day, establishing the geometry used ever since. The Hydraulic Institute, founded in 1917, standardized pump testing, performance curve presentation, and the definitions of head, NPSH and efficiency that make manufacturer curves comparable and let a calculated TDH be matched against a published pump curve.