Many have heard of the famous Leaning Tower of Pisa experiment that was reportedly conducted in 1589 by Galileo Galilei. The experiment was devised to overturn the long-held view that objects fall to Earth at rates of speed that are proportional to their weight. In other words, heavier objects should fall faster than lighter ones.
As the story goes, Galileo stood at the very top of the tower and held a heavy ball in one hand and a lighter ball in the other. He then released both balls simultaneously. As he predicted, both balls hit the ground at the same time. Even today, this result seems to fly in the face of common sense.
Let’s mentally reverse this experiment by now throwing these same balls upward (each at the same speed) from the ground. If we neglect air resistance, then both balls will slow down at the same rate as they travel upward. Eventually, both balls with stop momentarily at the exact same height above the ground.
An object that is moving (thrown) in the opposite direction of a constant force will only travel so far before it stops. On Earth, if we throw an object upward with an initial velocity (V) it will immediately start slowing down due to the deceleration of gravity. The height (H) the object will attain can be calculated using the following equation:
This is one of the equations of motion. If we apply it to a ball being thrown upward on the Earth then:
H= vertical distance the ball will travel (m or ft)
V= initial vertical velocity of the ball (m/s or ft/s)
g= deceleration due to gravity (9.81 m/s2 or 32.2 ft/s2
How this relates to pump head loss
Simply put, a pump impeller energizes a fluid by throwing it. Let’s neglect the complicated vector analysis that is taking place at the outer tip of the impeller vane. In doing so, we can consider the fluid’s exit velocity (from the pump) the same as the impeller’s peripheral speed.
Let’s use a centrifugal pump that is running at 1750 rpm with a 6” diameter impeller. We will assume the fluid’s exit velocity is the same as the impeller’s peripheral speed (about 46 ft/s). Therefore, if we neglect resistance, this liquid should travel (on Earth) vertically about:
Effects of an object’s mass
As we have noted, the weight of the ball (or fluid) makes no difference to the final height it will attain. But, we all know nothing in life is free! Imagine for a moment holding a baseball in one hand and a bowling ball in the other. We now know that if we throw both balls upward at the same speed they will reach the same height at the same time. But it will take much more effort to throw the heavier ball. In fact, the amount of effort will be directly proportional to the mass of the ball.
In the above case of the baseball and the bowling ball, what if we were to put our hand in the way of each ball’s path? The bowling ball would exert more force on our hand than the baseball. Now, let’s look at two streams of fluid: one, petroleum and the other, water. The weight of petroleum is about 80% that of water (specific gravity = 0.8). If we were able to measure the pressure of each stream of fluid at the same relative location, what would it show?
The petroleum’s pressure reading should always be 80% of the water stream’s reading. So, even though the head of the two liquids is the same, the pressure that it exerts depends on its density (weight/volume).
Specific gravity and centrifugal pump curves
Figures 1 and 2 show two curves for the same pump model. The only difference is the specific gravity of the fluid. Note that pressure values (PSI) and the location of the horsepower lines vary between the curves, while the head scale stays the same.
John Brooks Company, in partnership with Gorman-Rupp Canada, has been providing on-site and “manufacturer-based” certified training for several decades. Since that time, several hundred operators have successfully completed the “Fundamentals of Pumping” (MOECC ID 12158) training. This day-long course incorporates a balanced blend of theoretical learning and practical “hands on” factory equipment.
Attendees work with Gorman-Rupp’s self-priming “glass-face” pump which allows them to see inside an actual pump while it is operating. This allows for a practical demonstration and study of pump priming, air entrainment, suction/discharge cavitation, system curves and advanced trouble-shooting techniques from a whole new perspective.
This article appears in ES&E Magazine’s December 2019 issue.