EDA, Incorporated Sizing a Pump 
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To Size a Pump To size a pump or determine its total head, a calculation of the amount of fluid friction is required. Viscosity is the fluid property responsible for friction. The following is a brief discussion of viscosity. VISCOSITY The Definition of Absolute (or Dynamic) Viscosity. Many years ago, Isaac Newton investigated the fluid property called viscosity. He set up an experiment designed to measure viscosity. The experiment consisted in the interaction of two plates separated by a short distance, one fixed and one moving with fluid between. He theorized that it required a force F to move the top plate at a given velocity v. If the top plate was moving at velocity v, he deduced that the fluid layer just underneath the plate must be moving at the same velocity or else the plate would be skipping over the fluid surface. In addition, force F can only be produced if the top layer of fluid is attached to the top plate and the bottom layer to the bottom plate. Since the bottom plate is not moving, the bottom fluid layer is also not moving or has zero velocity. Therefore, the fluid layers between the moving surface and the fixed one have different velocities. Each layer of fluid is traveling at a different speed. It is this speed variation (or velocity gradient dv/dy, see Figure Al) that is the cause of viscosity and is responsible for shearing the fluid internally. Newton's assumption was that the velocity gradient is independent of viscosity. In other words, a force twice as large would be required to move the fluid twice as fast, meaning there must be a constant relationship between the force F required to move the fluid and the rate of shear. Alternatively, in mathematical form, the force F is proportional to the velocity gradient dv/dy:.
The constant A/K is called the viscosity of the fluid and is represented by the Greek letter m . The value of m will determine the magnitude of the shearing force F. Fluids with higher viscosities will require a greater shearing force for the same velocity differential. Since, the experiment should be valid for fluid bodies of any size, then the tangential stress t = F/A is a more appropriate parameter to relate to viscosity. The term m is known as the absolute viscosity of the fluid (see equation Al). The velocity gradient dv/dy is known as the rate of shear. Newton could not test his hypothesis because of experimental difficulties. Many years later, Poiseuille (1849) developed an experimental method that consisted in measuring the flow of liquid in a small tube and relating the pressure driving the fluid through the end of the tube to the flow and viscosity. Poiseuille's experimental apparatus verified the correctness of Newton's hypothesis. Newton's viscosity equation describes a class of fluids that came to be known as Newtonian fluids. Many fluids behave in this fashion (see Table A2). The unit of absolute viscosity is the Poise (or centipoises), in honor of Poiseuille. One (1) centipoises (the unit symbol is cP) is the viscosity of water at 68 ^{0}F making it easy to compare the viscosity of various fluids to that of water. Many fluids do not behave in the wellordered fashion of Newtonian fluids. These are known as nonNewtonian fluids. These fall in several categories (see Table A2) depending on what shape the tangential stress vs. velocity gradient takes. For these fluids, the velocity gradient is dependent on the viscosity. That is, the velocity affects the viscosity resulting in a much higher (or in some cases lower) rate of shear than for a Newtonian fluid. A typical household product will help illustrate this point, try the following experiment. Make a solution of cornstarch and water, approximately 1 part water to 2 parts cornstarch. Mix well into a large shallow bowl. Try moving this fluid rapidly around with your fingers. The faster you try to move through the fluid, the higher the resistance. If you move your fingers fast enough they will skip over the surface. At that rate of shear, the solution almost behaves as a solid, when the fingers are moved slowly, the solution behaves as expected offering little resistance. Compare this behavior to another fluid that seems equally thick, such as molasses (molasses is not considered a Newtonian fluid, however it is much closer to being Newtonian than a starch solution). The molasses flows readily no matter how fast the movement. This is what is meant by viscosity being dependent on rate of shear. This explains why centrifugal pumps with their high rate of shear are not suitable for nonNewtonian fluids (i.e. yield pseudoplastic or pseudoplastic). A pump operating at low speed, of the fixed displacement type is more appropriate. Kinematic viscosity A term frequently used in fluid mechanics (for example in the definition of the Reynolds number) is the Kinematic viscosity n . The relationship between the absolute and Kinematic viscosity is: The Kinematic viscosity of water at 68 ^{0}F is 1 centistokes (cSt), and was named in honor of G.G. Stokes of the NavierStokes equation fame.
Table A2 Rheological properties of Fluids
________________________________________________ For free calculations go to the Calculator page. The calculators should be used with caution. Many of these calculators are not verified and are only intended to provide a starting point in performing a design calculations. All final design calculations should be performed using verified and validated programs or calculators that have documented evidence of the verification and validation. ________________________________________________ _______________________________________________ Company ProfileEDA, Incorporated provides qualityengineering services on time, on schedule and within budget. EDA, Inc. is able to do this by performing the work correctly the first time. We accept the most challenging problems and look forward to working with the client as a team member. EDA believes that the client should be an active participant in the work process to ensure that the product is commensurate with client expectations and is delivered within schedule and budget constraints. EDA, Inc. belongs to the American Society of Mechanical Engineers (ASME), the National Society of Professional Engineers (NSPE), the Society of Instrument Control Engineers, Society of Professional Engineers (ISA) and the American Nuclear Society (ANS). For more information on EDA, Incorporated services, please contact Client Service Manager at: Client Service Manager EDA, Inc. 6397 True Lane Springfield, VA 22150
or email the Client Service Manager at SiteManager@edasolutions.com . 
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