Cheat Sheets: Energy, Work, & Power

Larry Bachus

The amazing James Watt was born in 1736 at the dawn of the industrial revolution. He was reared and educated in the coal and iron mining region of Scotland. In school, James studied math and prepared for a career as an instrumentation technician. He eventually became a mechanical engineer. His mission in life was to see machines replace human and animal labor.

Mining was, and still is, a labor intense industry. For tasks beyond the ability of a grown miner, the mining industry bred especially small horses that could go into the mines and do the pulling and hauling that a grown man could not do. It was one of man’s early attempts at genetic manipulation.

For menial labor, children were sent into the mines. Before the Child Labor Laws, children were used in the bilges of the mines because they had small lungs and didn’t consume the air/oxygen that a full-grown miner would consume.

The spinning balls atop James Watt’s infamous “Old Sally” 150-Hp steam engine serve as an early example of centrifugal regulation for industry. Because most mines are dug below the water table, and sometimes below sea level, many mines would eventually flood if it were not for the children and ponies that removed the water from the mines. The children would take horsehides and cowhides down into the bilge of a mine and sink the hides in the accumulating water. Up top, through a secondary mine shaft, a horse was harnessed to a rope through a pulley under a support frame. The rope was lowered through the secondary shaft down into the bilge of the mine. Down below, the children would attach the cowhide to the rope and the horse above would pull the hide into a bag of bilge water. Then the horse would march forward, physically lifting the water bag up out of the mine. The bilge water was dumped out up above, down the side of the mountain, and the process would begin again. Of course, the water dumped out of the bag eventually filtered again into the bilge of the mine. With pity toward the children and the workhorses, James decided to replace the human and animal labor in the mines with a steam engine. James began by defining terms and establishing standards. James defined “energy” as the “capacity to perform work.” James said “work” was defined as “a force exerted over a distance.” And James defined “power” as “work performed within a certain timeframe.” Many people use and interchange the terms “energy,” “power,” and “work” indiscriminately in conversation. But actually, each of these terms have precise definitions. Here are some examples: I have enough “energy” in my biceps muscle to pick up a 100-pound weight. This is the capacity to perform work. If I lift a 20-pound weight up five feet into the air, I’ve done 100 foot-pounds of “work.” Likewise, if I lift 10 pounds 10 feet, or five pounds 20 feet, or 100 pounds one foot, then I’ve done 100 foot-pounds of work. If I lift 50-pounds two feet in one second, this is “power.”

Because James Watt wanted his machines to do more work than a grown man, and because a horse is stronger than a man, he began by establishing what a horse could do. He harnessed a mine draft horse to a support frame and a platform and put some children and men onto the platform. The horse lifted 550 pounds of weight a distance of 10 feet in 10 seconds. So James Watt declared that 550 foot/pounds per second is one “horsepower.” It is because of James Watt’s scientific effort that electric motors, internal combustion engines, turbines, boilers, jet engines, rocket engines, etc. are rated in horsepower. If James Watt had been raised in India, we might have the term “elephant power.” If James had been from Australia, we might rate engines in “kangaroo power.” Oh yes, James went to his grave with an important part of the formula. He never told anyone what the size of his test horse was. So we don’t know if it was a Shetland pony, a mule, or a Clydesdale.

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A pump’s work (output) is called Water Horsepower (WHp). It is a combination of elevation (called head rated in feet), and flow (rated in gallons per minute). Expressed as an equation:

WHp = H x Q/3960

Watt’s centrifugal regulator invention as seen on a steam tractor at an old farm equipment parade in South Africa.

The number 3,960 converts power into pump language. Put this into your “CHEAT SHEETS” and remember it. I’ll explain.

As stated earlier, one horsepower is 550 foot/pounds per second, and most pumps are rated in flow per minute (GPM). Multiply 550 by 60 seconds in a minute, and we have 33,000 foot/pounds per minute. Next, a gallon of water (at sea level and 70 F) weighs 8.333 pounds. Divide the 33,000 ft. pounds by 8.333 pounds per gallon and we have 3,960. The 3,960 is a horsepower expressed in pump terminology.

In James Watt’s day, water was the only liquid that needed to be moved in large quantities. This was cold water for bathing, drinking, and lifting up from the bilge of a coal mine. Beer, paint, solvents, milk, lamp oil, acid, and whiskey were made in bottles, buckets, or casks and carried from one place to another.

As technology advanced, pumps were employed to transport liquids other than water. Another element, the specific gravity was incorporated into the basic WHp formula:

WHp = H x Q x sp. gr./3960

The above is the basic formula for water horsepower and for liquids other than water. It’s a good number, but not useful. We never need to know this number.

Frequently, we need to know a variation of this number. We need to know the BHp, or brake horsepower to drive the pump. If the pump were 100 percent efficient, then the BHp would be equal to the WHp. Pumps are not 100 percent efficient. So, this brings us to another variation on the formula. Now we have:

BHp = H x Q x sp. gr./3960 x eff.

This is a relatively easy formula to understand. Lets work with it a little.

Imagine that we have a pumping system that requires 600 GPM of water, while generating 40 PSI. In pump terminology, 40 PSI is the same as 92 feet of head (We know this from a previous CHEAT SHEETS column (Feb. ’08, page 40)). Let’s say our pump is 77 percent efficient. The specific gravity of water is 1.0. To apply the formula, the H = 92, the Q is 600, and the efficiency = 77 percent. Now we have:

BHp = 92 x 600 x 1.0/3960 x 77%
BHp = 18.1 horses

We need 18.1 horses to power this pump. We must install a 20-Hp motor onto this pump because no one makes an 18.1 Hp motor. The monthly electric bill will be based on 13.5-kilowatts (Kw = Hp x .746).

Many pump specifications don’t mention or require efficiency. The specs mostly deal with the needs of the system, meaning the 92 ft. @ 600 GPM. Purchasing agents can fall into the price trap.

Suppose two different suppliers have a pump that meets the system’s requirements (92-ft. @ 600 GPM). What if one pump sells for $800 less than the other pump? What if we could save $800 by buying another comparable pump that meets the needs of the system. If the cheaper pump were 60 percent efficient, we’d have some different horsepower figures:

BHp= 92 x 600 x 1.0/3960 x 60%
BHp = 23.2 horses

The cheaper pump requires 23.2 horsepower. The monthly electric bill will be based on 17.3 Kw, and you must buy a 25 Hp motor to operate the cheaper pump with the reduced efficiency.

The difference is 5.1 horses or 3.8 kilowatts. If the pump runs for a year, this would mean an additional $3,332 dollars per year in electricity to run the inefficient pump at 10¢ per kilowatt/hour. And this $3,332 would be on top of the additional cost for the larger (25-Hp) motor. How do you feel about your $800 savings now?

An even cheaper pump might perform the same work and be only 50 percent efficient. This pump would burn 27.8 horses of electricity, and it would require a 30-Hp motor. If it ran 24-hours per day, this would be an additional $6,340 in the electric bill per year compared to the first pump.

If you’ve been following the Pump Guy in Flow Control magazine, you know I started my maintenance career as an apprentice grunt in a Birmingham steel mill. And you also know I was a pump mechanic in the Navy. I’ve stood by helpless while my bosses, chiefs, and purchasing agents made these poor decisions. And guess who was stuck with the maintenance on those cheap pumps?

Today, many government agencies send their engineers and techs to the Pump Guy Seminars. And the engineers all say, “But Larry, you don’t understand; we’re under instructions to buy the cheapest pump based on a competitive bid.” It is truly sad.

These are good people, and they understood the information, but they have their instructions. Who is responsible for this? Remember the efficiency next time you go to buy a pump.

Larry Bachus, founder of pump services firm Bachus Company Inc., is a regular contributor to Flow Control magazine. He is a pump consultant, lecturer, and inventor based in Nashville, Tenn. Mr. Bachus is a member of ASME and lectures in both English and Spanish. He can be reached at [email protected] or 615 361-7295.

www.bachusinc.com