Dynamic Pressure – Velocity Pressure

Dynamic Pressure – Velocity Pressure

In general, pressure is a measure of the force exerted per unit area on the boundaries of a substance. The term dynamic pressure (sometimes called velocity pressure)  is associated with fluid flow and with the Bernoulli’s effect, which is described by the Bernoulli’s equation:

Bernoulli Theorem - Equation

This effect causes the lowering of fluid pressure (static pressure) in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy (dynamic pressure – ½.ρ.v2) must increase at the expense of pressure energy (static pressure – p).

As can be seen, dynamic pressure is dynamic pressure is one of the terms of Bernoulli’s equation. In incompressible fluid dynamics, dynamic pressure is the quantity defined by:

dynamic pressure - formula

The simplified form of Bernoulli’s equation can be summarized in the following memorable word equation:

static pressure + dynamic pressure = total pressure (stagnation pressure)

Total and dynamic pressure are not pressures in the usual sense – they cannot be measured using an aneroid, Bourdon tube or mercury column.

To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure. The term static pressure is identical to the term pressure, and can be identified for every point in a fluid flow field. Dynamic pressure is the difference between stagnation pressure and static pressure.

Dynamic Pressure and Pressure Loss

PLC - Pressure loss coefficient - equationsDynamic pressure is closely related to pressure losses. In the practical analysis of piping systems the quantity of most importance is the pressure loss due to viscous effects along the length of the system, as well as additional pressure losses arising from other technological equipments like, valves, elbows, piping entrances, fittings and tees. By observation, the  head loss is roughly proportional to the square of the flow rate in most engineering flows (fully developed, turbulent pipe flow). In fact, the  head loss is directly proportional to the dynamic pressure.

The constant of proportionality is the pressure loss coefficient. The pressure loss coefficient is noted K or ξ  (pronounced “xi”). This coefficient characterizes pressure loss of a certain hydraulic system or of a part of a hydraulic system. It can be easily measured in hydraulic loops. The pressure loss coefficient can be defined or measured for both straight pipes and especially for local (minor) losses. For example, the pressure loss coefficient ξ = 4.9  causes that the pressure drop will be about 4.9 times the dynamic pressure.

 
References:
Heat Transfer:
  1. Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley & Sons, Incorporated, 2011. ISBN: 9781118137253.
  2. Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.
  3. Fundamentals of Heat and Mass Transfer. C. P. Kothandaraman. New Age International, 2006, ISBN: 9788122417722.
  4. U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. DOE Fundamentals Handbook, Volume 2 of 3. May 2016.

Nuclear and Reactor Physics:

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  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Pressure