Chapter 15. -PUMPS AND FORCED DRAFT BLOWERS 



Basically, head is a measure of the pressure 

 exerted by a column or body of liquid because of 

 the weight of the liquid. In the case of water, we 

 find that a column of fresh water 2.309 feet high 

 exerts 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 of 

 1 psibecauseof its own weight. Thus, a reference 

 to a head of so many feet of water does imply a 

 reference to the pressure exerted by that water. 



The situation is somewhat different when we 

 have a horizontal pipe through which water is 

 being pumped. In this case, the head is calculated 

 as the vertical distance that would correspond to 

 the pressure. If the pressure in the horizontal 

 pipe is 1 psi, then the head on the liquid in the 

 pipe is 2.309 feet. Further calculations show that 

 a head of 1 foot corresponds to a pressure of 

 0.433 psi. 



The relationship between head and energy can 

 be clarified by considering that (l)workisa form 

 of energy— mechanical energy in transition; (2) 

 work is the product of a force times the distance 

 through which it acts; and (3) for liquids, the work 

 performed is equal to the volume of liquid moved 

 times the head against which it is moved. Thus 

 the head relationships actually indicate some of 

 the energy relationships for a given quantity of 

 liquid. 



VELOCITY HEAD. - The head required to 

 impart velocity to a liquid is known as velocity 

 head. It is equivalent to the distance through 

 which the liquid would have to fall in order to ac- 

 quire the same velocity. If we know the velocity 

 of the liquid, we can compute the velocity head 

 by the formula 



V 2g 

 where 



H = velocity head, in feet 



V = velocity of liquid, in feet per second 



g = acceleration due to gravity (32.? feet per 

 second per second) 



ity. However, velocity head does not represent a 

 total loss, since at least a portion of the velocity 

 head can always be reconverted to static pres- 

 sure head. 



FRICTION HEAD. -The force or pressure 

 required to overcome friction is also obtained at 

 the expense of the static pressure head. Unlike 

 velocity head, however, friction head cannot be 

 "recovered" or reconverted to static pressure 

 head, since fluid friction results in the conver- 

 sion of mechanical kinetic energy to thermal 

 energy. Since this thermal energy is usually 

 wasted, friction head must be considered as a 

 total loss from the system. 



BERNOULLI'S THEOREM. -At any point in 

 a system, the static pressure head will always 

 be the original static pressure head minus the 

 velocity head and minus the friction head. Since 

 both velocity head and friction head represent 

 energy which comes from the original static 

 pressure head, the sum of the static pressure 

 head, the velocity head, and the friction head at 

 any point in a system must add up to the original 

 static pressure head. This general principle, 

 which is known as Bernoulli's theorem , may also 

 be expressed as 



2 2 



P, V P V 



Z +-i+_i=Z +-?+-f+[J(U -U,)-Wk-JQ] 

 ' D 2g -^ D 2g ^ ' 



where 



Z = elevation, in feet 



P = absolute pressure, 

 foot 



D = density of liquid, in pounds per cubic foot 



V = velocity, in feet per second 



g = acceleration due to gravity (32.2 feet per 

 second per second) 



J = the mechanical equivalent of heat, 778 foot- 

 pounds per Btu 



U = internal energy, in Btu 

 Wk =work, in foot-pounds 



in pounds per square 



Q = heat transferred, in Btu 



In a sense, velocity head is obtained at the 

 expense of pressure head. Whenever a liquid is 

 given a velocity, some part of the original static 

 pressure head must be used to impart this veloc- 



When written in this form, Bernoulli's theo- 

 rem may be readily recognized as a special 

 statement of the general energy equation. The 

 bracketed term represents energy in transition 

 as work, energy in transition as heat, and the 



395 



