Principles of naval engineering - Historic Naval Ships Association

Chapter 15. -PUMPS AND FORCED DRAFT BLOWERSBasically, head is a measure of the pressureexerted by a column or body of liquid because ofthe weight of the liquid. In the case of water, wefind that a column of fresh water 2.309 feet highexerts a pressure of 1 pound per square inch.When we refer to a head of water of 2.309 feet,we know that the water is exerting a pressure of1 psibecauseof its own weight. Thus, a referenceto a head of so many feet of water does imply areference to the pressure exerted by that water.The situation is somewhat different when wehave a horizontal pipe through which water isbeing pumped. In this case, the head is calculatedas the vertical distance that would correspond tothe pressure. If the pressure in the horizontalpipe is 1 psi, then the head on the liquid in thepipe is 2.309 feet. Further calculations show thata head of 1 foot corresponds to a pressure of0.433 psi.The relationship between head and energy canbe clarified by considering that (l)workisa formof energy— mechanical energy in transition; (2)work is the product of a force times the distancethrough which it acts; and (3) for liquids, the workperformed is equal to the volume of liquid movedtimes the head against which it is moved. Thusthe head relationships actually indicate some ofthe energy relationships for a given quantity ofliquid.VELOCITY HEAD. - The head required toimpart velocity to a liquid is known as velocityhead. It is equivalent to the distance throughwhich the liquid would have to fall in order to acquirethe same velocity. If we know the velocityof the liquid, we can compute the velocity headby the formulawhereHV2g= velocity head, in feetV = velocity of liquid, in feet per secondg = acceleration due to gravity (32.? feet persecond per second)In a sense, velocity head is obtained at theexpense of pressure head. Whenever a liquid isgiven a velocity, some part of the original staticpressure head must be used to impart this veloc-ity. However, velocity head does not represent atotal loss, since at least a portion of the velocityhead can always be reconverted to static pressurehead.FRICTION HEAD. -The force or pressurerequired to overcome friction is also obtained atthe expense of the static pressure head. Unlikevelocity head, however, friction head cannot be"recovered" or reconverted to static pressurehead, since fluid friction results in the conversionof mechanical kinetic energy to thermalenergy. Since this thermal energy is usuallywasted, friction head must be considered as atotal loss from the system.BERNOULLI'S THEOREM. -At any point ina system, the static pressure head will alwaysbe the original static pressure head minus thevelocity head and minus the friction head. Sinceboth velocity head and friction head representenergy which comes from the original staticpressure head, the sum of the static pressurehead, the velocity head, and the friction head atany point in a system must add up to the originalstatic pressure head. This general principle,which is known as Bernoulli's theorem , may alsobe expressed as2 2P, V P VZ +-i+_i=Z +-?+-f+[J(U -U,)-Wk-JQ]where'D 2g -^ D 2g ^ 'Z = elevation, in feetP = absolute pressure, in pounds per squarefootD = density of liquid, in pounds per cubic footV = velocity, in feet per secondg = acceleration due to gravity (32.2 feet persecond per second)J = the mechanical equivalent of heat, 778 footpoundsper BtuU = internal energy, in BtuWk =work, in foot-poundsQ = heat transferred, in BtuWhen written in this form, Bernoulli's theoremmay be readily recognized as a specialstatement of the general energy equation. Thebracketed term represents energy in transitionas work, energy in transition as heat, and the395