Manual Theory and Applications of Nonviscous Fluid Flows

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Recommend to Librarian. A simple lecture demonstration has been developed which demonstrates how viscosity dramatically changes fluid flow in a pipe.

Water in an open reservoir is first allowed to escape through circular apertures near the bottom of the reservoir, which shows volume flow rates proportional to the area of the aperture for a low viscosity fluid. This is direct visual confirmation of the Hagen—Poiseuille prediction that volume flow rates scale as the fourth power of the tube radius for laminar flow.

Overcoming experimental complications involving vena contracta and entry length issues is discussed, along with detailed measurements and fits to theory. The greater the pressure differential between two points, the greater the flow rate. This relationship can be stated as. If viscosity is zero, the fluid is frictionless and the resistance to flow is also zero. Comparing frictionless flow in a tube to viscous flow, as in Figure We can see the effect of viscosity in a Bunsen burner flame, even though the viscosity of natural gas is small.

This equation is called Poiseuille's law for resistance after the French scientist J. Poiseuille — , who derived it in an attempt to understand the flow of blood, an often turbulent fluid.

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After all, both of these directly affect the amount of friction encountered—the greater either is, the greater the resistance and the smaller the flow. This exponent means that any change in the radius of a tube has a very large effect on resistance.

This equation describes laminar flow through a tube. It is sometimes called Poiseuille's law for laminar flow, or simply Poiseuille's law.

Suppose the flow rate of blood in a coronary artery has been reduced to half its normal value by plaque deposits. By what factor has the radius of the artery been reduced, assuming no turbulence occurs?

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We need to compare the artery radius before and after the flow rate reduction. With a constant pressure difference assumed and the same length and viscosity, along the artery we have. This decrease in radius is surprisingly small for this situation. The circulatory system provides many examples of Poiseuille's law in action—with blood flow regulated by changes in vessel size and blood pressure.

Blood vessels are not rigid but elastic. Adjustments to blood flow are primarily made by varying the size of the vessels, since the resistance is so sensitive to the radius. During vigorous exercise, blood vessels are selectively dilated to important muscles and organs and blood pressure increases.

This creates both greater overall blood flow and increased flow to specific areas. Conversely, decreases in vessel radii, perhaps from plaques in the arteries, can greatly reduce blood flow.

Simple trick to understand Continuity & Bernoulli's Equation. JEE Physics XI Fluids

Another example comes from automobile engine oil. If you have a car with an oil pressure gauge, you may notice that oil pressure is high when the engine is cold. Motor oil has greater viscosity when cold than when warm, and so pressure must be greater to pump the same amount of cold oil. An intravenous IV system is supplying saline solution to a patient at the rate of 0. What pressure is needed at the entrance of the needle to cause this flow, assuming the viscosity of the saline solution to be the same as that of water?

The gauge pressure of the blood in the patient's vein is 8.

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Substituting this and the other known values yields. This pressure could be supplied by an IV bottle with the surface of the saline solution 1.

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You may have noticed that water pressure in your home might be lower than normal on hot summer days when there is more use. This pressure drop occurs in the water main before it reaches your home.

Theory and Applications of Nonviscous Fluid Flows

Let us consider flow through the water main as illustrated in Figure Resistance will be much greater in narrow places, such as an obstructed coronary artery. This is how water faucets control flow. Plaque in an artery reduces pressure and hence flow, both by its resistance and by the turbulence it creates. Pressure created by the heart's two pumps, the right and left ventricles, is reduced by the resistance of the blood vessels as the blood flows through them.

This book is aimed at researchers and students alike as it also provides all the necessary basic knowledge about fluid dynamics. It would also be a valuable supplemental text for a post-master course in fluid mechanics. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.

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