Water Hammer - Expression For The Excess Pressure Due To Water Hammer

Expression For The Excess Pressure Due To Water Hammer

When a valve with a volumetric flow rate Q is closed, an excess pressure δP is created upstream of the valve, whose value is given by the Joukowsky equation:

In this expression:

  • overpressurization δP is expressed in Pa;
  • Q is the volumetric flow in m3/s;
  • Zh is the hydraulic impedance, expressed in kg/m4/s.

The hydraulic impedance Zh of the pipeline determines the magnitude of the water hammer pulse. It is itself defined by:

with:

  • ρ the density of the liquid, expressed in kg/m3;
  • A cross sectional area of the pipe, m2;
  • Beff effective modulus of compressibility of the liquid in the pipe, expressed in Pa.

The latter follows from a series of hydraulic concepts:

  • compressibility of the liquid, defined by its adiabatic compressibility modulus Bl, resulting from the equation of state of the liquid generally available from thermodynamic tables;
  • the elasticity of the walls of the pipe, which defines a modulus of equivalent compressibility Beq. In the case of a pipe of circular cross section whose thickness e is small compared to the diameter D, the equivalent modulus of compressibility is given by the following formula: ; in which E is the Young's modulus (in Pa) of the material of the pipe;
  • possibly compressibility Bg of gas dissolved in the liquid, defined by:
    • γ being the ratio of specific heats of the gas
    • α the rate of ventilation (the volume fraction of undissolved gas)
    • and P the pressure (in Pa).

Thus, the effective compressibility modulus is:

As a result, we see that we can reduce the water hammer by:

  • increasing the pipe diameter at constant flow, which reduces the inertia of the liquid column;
  • choosing to use a material with a reduced Young's modulus;
  • introducing a device that increases the flexibility of the entire hydraulic system, such as a hydraulic accumulator;
  • where possible, increasing the percentage of undissolved air in the liquid.

Read more about this topic:  Water Hammer

Famous quotes containing the words expression, excess, pressure, due, water and/or hammer:

    “Removed from its more restrictive sense, masturbation has become an expression for everything that has proved, for lack of human contact, to be void of meaning. We have communication problems, suffer from egocentrism and narcissism, are frustrated by information glut and loss of environment; we stagnate despite the rising GNP.”
    —Günther Grass (b. 1927)

    “Where an excess of power prevails, property of no sort is duly respected. No man is safe in his opinions, his person, his faculties, or his possessions.”
    —James Madison (1751–1836)

    “Amid the pressure of great events, a general principle gives no help.”
    —Georg Wilhelm Friedrich Hegel (1770–1831)

    “Rationalists are admirable beings, rationalism is a hideous monster when it claims for itself omnipotence. Attribution of omnipotence to reason is as bad a piece of idolatry as is worship of stock and stone believing it to be God. I plead not for the suppression of reason, but for a due recognition of that in us which sanctifies reason.”
    —Mohandas K. Gandhi (1869–1948)

    “Not all the water in the rough rude sea
    Can wash the balm off from an anointed king;
    The breath of worldly men cannot depose
    The deputy elected by the Lord.”
    —William Shakespeare (1564–1616)

    “Many hammer all over the wall and believe that with each blow they hit the nail on the head.”
    —Johann Wolfgang Von Goethe (1749–1832)