# Pumps: Check "Standard Conditions"

## Otherwise you risk using the wrong value for density in calculations.

"The pump discharge pressure will change depending on the liquid," said the client's maintenance engineer. For the sake of decorum, I remained quiet and kept a poker face despite knowing he was wrong. For years, I had specified pumps in psi *not* head to avoid such confrontations. This and other misconceptions seem to run amok in engineering.

First, let's consider the pump head. In my opinion, head, where used, should be in feet of water at 68°F. Those are the conditions the Hydraulic Institute, an association of pump makers and users, chooses when it talks about pumps. The trouble with many pump curves is that they imply water is at 68°F but never state that. This leaves room for mischief.

When you have discharge head (DH) and suction head (SH) in pressure, e.g., psi, the total dynamic head (TDH) is a fixed quantity (TDH = DH – SH). The pressure depends upon the specific gravity (SG) of the liquid versus that of water at 68°F. You might argue that using the density of water at 60°F would be more appropriate if the operating company uses that basis — but, remember, we're ordering a pump! If the head is in ft-liquid, as it is during energy balance calculations, then the pressure, unless converted, isn't known yet. If stated as a result in pressure, the value remains constant.

Water density introduces another potential snag. Water at 68°F has a specific gravity of 0.9983,

*not*1.0000, so let's discuss that misconception. "Cameron Hydraulic Data," 19th ed., takes considerable pains at the beginning of Section 4 to define the specific gravity of water. The oil industry, including the American Petroleum Institute, uses 60°F as the reference temperature for specific gravity; simulation results for "standard conditions" reference 60°F. Water's specific gravity at 60°F is 0.9991; its density is 62.367 lb/ft3, according to the U.S. National Institute of Standards and Technology (NIST). In the International System of Units, the reference temperature is 25°C (77°F); water has a specific gravity of 0.9971 and a density of 62.25 lb/ft

^{3}at that temperature. Other groups use 4°C (39.2°F), the temperature at which the specific gravity actually is 1.000, the maximum value; density is 62.425 lb/ft3. As "Cameron Hydraulic Data" and other engineering books point out, the variety of so-called standard conditions can cause confusion. So, it's best to define the reference conditions at every use, regardless of how pedantic that may seem.

While we're on the topic of the misuse of specific gravity, let's discuss density calculations with vapors. Gas specific gravity often is defined in terms of the gas density divided by the density of air at a standard condition (SC): SG = ρ

*/ρ*

_{gas}*. Numerous online references use cute shortcut methods, e.g., SG = molecular weight of the gas/molecular weight of air. This definition is at best sloppy engineering and at worst completely erroneous. If the temperature increases, the density should decrease but won't based on this unsound over-simplification, especially when the compressibility factor, Z, is not 1. The "Standard Handbook of Petroleum and Natural Gas Engineering," 2nd ed., p. 2-19, describes gas specific gravity as the density of the gas at a specified temperature and pressure divided by the density of air at a standard condition. Again, there's quite a variety of SCs.*

_{air-SC}The NIST and the International Union of Pure and Applied Chemistry take 1 bar (0.987 atm, 14.504 psia) at 0°C (32°F) as standard pressure and temperature (STP) while acknowledging informal standards for ambient temperature and pressure (SATP). NIST uses 20°C (68°F) at 1 atm for SATP. The gas industry relies on so-called International Standard Metric Conditions, 1 atm (14.696 psia) and 15°C (59°F), for natural gas and other refinery gases. For a listing of SCs of some organizations and government entities, including the U.S. Environmental Protection Agency, see: http://en.wikipedia.org/wiki/Standard_conditions_for_temperature_and_pressure. Another useful source is: www.thefreelibrary.com/A+twenty-first+century+molar+mass+for+dry+air.-a0186399836.

Don't confuse STP and SATP with standard state used in thermodynamics. Enthalpy, heat capacity and entropy all require a reference state. Most tabular data for these thermodynamic functions are at 25°C (77°F), although 0°C also has been used as reference. The gas pressure at thermodynamic reference state usually is such that the gas behaves as perfect gas.

DIRK WILLARD is a Chemical Processing contributing editor. He recently won recognition for his Field Notes column from the ASBPE. Chemical Processing is proud to have him on board. You can e-mail him at dwillard@putman.net

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## Comments

Submitted by John O'Sullivan on Mon, 04/21/2014 - 14:26

While Mr. Willard's comments on Standard Conditions themselves need everyone's attention, he does no one any favors with his very bollixed description of pump head. The first three paragraphs of his "Pumps: Check "Standard Conditions" (Chem Proc Apr 8, 2014) reveal a very basic misunderstanding of the terms involved in pumping. In fact the"client's maintenance engineer" in the first line who Mr. Willard "knew was wrong" was absolutely correct. Per Streeter and Wylie's classic, "

Fluid Mechanics" (7th Edition), head is defined as the "potential energyper unit weight" produced by or used by a turbomachine. Potential energy is defined as the product of the density of the fluid and the distance above a datum -- in the case of pump head, the elevation of the source liquid. That is, head = density X distance / unit weight (i.e., density). Thus, the head produced by a pump at any given volumetric flow rate is only a distance, and completely independent of the density of the liquid. It is one of the minor miracles of vector mathematics that, regardless of the liquid being pumped, the machine will produce the same head for the same volumetric flow rate and rotational speed.The

it takes to do this does vary with the liquid's density, but the head itself is independent of density.powerOnly the power curve needs correction for the density.(There are other corrections which have to be made for differences in viscosity and compressibility, but these are quite secondary except for the most viscous or compressible of liquids, and not germane to our discussion here.)The first sentence of Paragraph 3, "When you have discharge head (DH) and suction head (SH) in pressure, e.g., psi, the total dynamic head (TDH) is a fixed quantity (TDH = DH – SH)" combines all the confusion into a single line. Firstly, you should never express pump performance in terms of pressure. It is always a head, that is, a height to which the liquid could be lifted by the pump operating at its given speed and volumetric flow rate. And secondly, regarding the last sentence of that paragraph, it is not the stated difference in

psithat is a fixed quantity; it is thehead in ftor meters that is the fixed quantity.The Hydraulic Institute (HI) itself (Page 68 of the 14th Edition of their "

Standards for centrifugal, rotary & reciprocating pumps") says, "The unit for measuring head shall be the foot....All pressure readings must be converted into feet of the liquid being pumped."It is only in discussing output

horsepower(Page 90) that HI mentions the words, "irrespective of the specific weight", but that is only if you have expressed your total head in pressure terms (in violation of their Page 68 ;-). Their equation for output horsepower is whp = (pounds of liquid pumped per min) X (total head in feet of liquid) / 33,000. Of course, the pounds of liquid = the cubic feet X the density.I hope this helps clarify the issue that Mr. Willard was trying to present in his first three paragraphs.

John D. (Jack) O'Sullivan, P.E., F.ASCE (licensed in California, Michigan, Texas) (NOTE: This opinion is mine, and the company I work for has no involvement in my expressing it.)

Reply

Submitted by Jeff Willard on Mon, 04/21/2014 - 16:07

I want to thank John O’Sullivan for his thorough response. He brings up some good points. I frequently wish I had more time in the column to provide such detail.

Regarding the first point, pressure versus head, in ft-liquid being pumped: psi is acceptable except when doing a calculation to size a pump. Pressure can easily be converted to ft-liquid being pumped:

PSI = Head in ft * SG/2.31 (Head in ft-fluid pumped; SG with reference to water at 68oF) The conversion factor, 2.31, changes depending on the reference temperature. If I express a DP = 20 psi, then if I am pumping propane with a specific gravity of 0.5 the ft-propane is 92.4 ft-propane; for water, with a specific gravity of 1 (at 68oF), we have only 45.2 ft-water. The pressure stays the same but the ft-liquid changed.

Reference: Cameron Hydraulic Data, page 1-10.

As for TDH = DP - SP. This expression was from a CEP article and this conclusion is also supported by the McNally Institute. If the SP decreases, the DP must increase to compensate to provide the same TDH. As a result, the pump will move left on its curve and the pumped flow will decrease to maintain the energy equation. Refer to:

http://www.mcnallyinstitute.com/10-html/10-12.html

I should also clarify one of statements later in the article. By reference, I meant that when the density of water at 14.696 psia and 60 F is used as the reference it is the term used in the denominator, e.g, for propane: 31.184/62.367 = 0.50.

Reply

Submitted by Jeff Willard on Sun, 04/27/2014 - 11:57

Hi should add a minor correction: DP should be TDH (total dynamic head) in my description of the feet of head for propane and water. I should also point out that Cameron Hydraulic Data Book mentions that the 2.31 commonly used in converting head to pressure relies on two things: a fixed barometric pressure; and, a reference temperature. Even Cameron is less than perfect in respecting reference state. In the barometric pressure table on page 8-4 of the 19th edition of Cameron (2010) you will find reference to the equivalent head of water at 75 F. This is while Cameron uses 65 F and 68 F in many places in the book. To convert the barometric pressure requires converting from the 75 F used in the barometric table to the reference temperature you happen to be using. This is an additional multiplication correction factor to the barometric table: SG(ref. T)/SG(75 F) * ft-liq for water. It is crucial to include barometric pressure, especially with blowers and compressors because disastrous designs can result. I remember having to respecify a compressor we were specifying for a job at 12,000 ft in China. Barometric pressure is critical especially in scrubbers and such. Here's a useful table for converting between feet of water and pressure, i.e., P = ft-water/C, or more properly from pg 1-10 of Cameron, P = ft-liquid *SG/C:

Barometric pressure: 14.696 psia -- sea level Temp. of reference -F Density of water Conv. Factor for ft-water 32 62.418 2.307 50 62.409 2.307 60 62.367 2.309 65 62.336 2.310 68 62.316 2.311 70 62.301 2.311 75 62.261 2.313 77 62.244 2.313 I hope this clarifies my discussion on Standard Conditions. The water's murky out there.

Reply

Submitted by John O'Sullivan on Wed, 05/21/2014 - 15:43

I agree completely with Mr Willard's 04/21/2014, 3rd paragraph statement that "If I express a DP = 20 psi, then if I am pumping propane with a specific gravity of 0.5 the ft-propane is 92.4 ft-propane; for water, with a specific gravity of 1 (at 68oF), we have only 45.2 ft-water. The pressure stays the same but the ft-liquid changed." BUT ... The truth of this statement hinges completely upon its first three words: "If I express ..." with special emphasis on the "I". The point I was trying to make -- and the point of "the client's maintenance engineer" who started this entire discussion -- was that

pumps do not "express" their abilities as pressure differences.Pumps express their abilities inhead.If a pump produces 100 feet of TDH at 1000 gpm when pumping water, then at the same rpm, it will also produce 100 feet of TDH if it's pumping 1000 gpm of propane or mercury. It will indeed take morepowerto pump the denser liquids, but for any given volumetric flowrate,the head difference will be the same regardless of what liquid is being pumped.Thepressure differencewill vary with the density. Finally, a careful reading of the McNally page that Mr Willard cited reveals no mention of pressure when discussing pump TDH. It is always "head" -- a wise choice. (Please note that this is not an endorsement of the McNally page, which contains a number of confusing statements, but at least it is consistent when speaking of pump head.) Good luck and God bless.Reply

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