Pg is the gage pressure and P is the absolute pressure. Unless otherwise specified, P is always the absolute pressure.
In terms of the new variables and the velocity heads V2/2g = hvi and V2/2g = hvo for the pump inlet and outlet velocity heads, respectively, TDH, designated as TDHabs, may also be expressed as
Note that habs is used rather than h. h is merely a relative value and would be a mistake if substituted into the above equation.
For static suction lift conditions, hi is always negative since gage pressure is used to express its corresponding pressure, and its theoretical limit is the negative of the difference between the prevailing atmospheric pressure and the vapor pressure of the liquid being pumped. If the pressure is expressed in terms of absolute pressure, then habs has as its theoretical limit the vapor pressure of the liquid being pumped.
Because of the suction action of the impeller and because the fluid is being lifted, the fluid column becomes "rubber-banded." Just like a rubber band, it becomes stretched as the pressure due to suction is progressively reduced; eventually, the liquid column ruptures. As the rupture occurs, the inlet suction pressure will actually have gone down to equal the vapor pressure, thus, vaporizing the liquid and forming bubbles. This process is called cavitation.
Cavitation can destroy hydraulic structures. As the bubbles which have been formed at a partial vacuum at the inlet gradually progress along the impeller toward the outlet, the sudden increase in pressure causes an impact force. Continuous action of this force shortens the life of the impeller.
The sum of the inlet manometric height absolute and the inlet velocity head is called the inlet dynamic head, idh (dynamic because this value is obtained with fluid in motion). The sum of the outlet manometric height absolute and the outlet velocity head is called the outlet dynamic head, odh. Of course, the TDH is also equal to the outlet dynamic head minus the inlet dynamic head.
In general, dynamic head, dh is
It should be noted that the correct substitution for the pressure terms in the above equations is always the absolute pressure. Physical laws follow the natural measures of the parameters. Absolute pressures, absolute temperatures, and the like are natural measures of these parameters. Gage pressures and the temperature measurements of Celsius and Fahrenheit are expedient or relative measures. This is unfortunate, since oftentimes, it causes too much confusion; however, these relative measures have their own use, and how they are used must be fully understood, and the results of the calculations resulting from their use should be correctly interpreted. If confusion results, it is much better to use the absolute measures.
Example 4.1 It is desired to pump a wastewater to an elevation of 30 m above a sump. Friction losses and velocity at the discharge side of the pump system are estimated to be 20 m and 1.30 m/s, respectively. The operating drive is to be 1200 rpm. Suction friction loss is 1.03 m; the diameter of the suction and discharge lines are 250 and 225 mm, respectively. The vertical distance from the sump pool level to the pump centerline is 2 m. (a) If the temperature is 20°C, has cavitation occurred? (b) What are the inlet and outlet manometric heads? (c) What are the inlet and outlet total dynamic heads? From the values of the idh and odh, calculate TDH.
Let the sump pool level be point 1 and the inlet to the pump as point 2.
Ad = cross-section of discharge pipe = -^D = n(a225 - = 0.040 m2
Therefore, Q = discharge = 1.3 (0.040) = 0.052 m3/s
Therefore, 0 + 0 + 0 + 0 - 1.03 + 0 = ,1059, - + 2 + —2
P2 Y = -3.087 m; because the pressure used in the equation is 0, this value represents the manometric head to the pump
At 20°C, Pv (vapor pressure of water) = 2.34 kN/m2 = 0.239 m of water Assume standard atmosphere of 1 atm = 10.34 m of water.
Therefore, theoretical limit of pump cavitation = - (10.34 - 0.239) = -10.05 m << -3.087
Cavitation has not been reached. Ans (b) Inlet manometric head = -3.087 m of water. Ans Apply the energy to the equation between the sump level and the discharge 30 m above
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