Who is poiseuille

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 4, we see that for a viscous fluid, speed is greatest at midstream because of drag at the boundaries. We can see the effect of viscosity in a Bunsen burner flame, even though the viscosity of natural gas is small.

Poiseuille — , who derived it in an attempt to understand the flow of blood, an often turbulent fluid. Figure 4. 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.

The radius r of a tube affects the resistance, which again makes sense, because the greater the radius, the greater the flow all other factors remaining the same. 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. 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? 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. 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.

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. Figure 5. The direction of flow is from greater to lower pressure. Flow rate increases with r 4 , the fourth power of the radius. 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 only unknown is P 2. P 1 is given as 8. 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. 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. Let us consider flow through the water main as illustrated in Figure 6. We can understand why the pressure P 1 to the home drops during times of heavy use by rearranging. During times of heavy use, the flow rate Q is large.

Thus P 1 must decrease. It is correct to think of flow and resistance as causing the pressure to drop from P 2 to P 1. Figure 6. During times of heavy use, there is a significant pressure drop in a water main, and P 1 supplied to users is significantly less than P 2 created at the water works. Resistance will be much greater in narrow places, such as an obstructed coronary artery.

For a given flow rate Q , the pressure drop will be greatest where the tube is most narrow. This is how water faucets control flow. Additionally, R is greatly increased by turbulence, and a constriction that creates turbulence greatly reduces the pressure downstream. Plaque in an artery reduces pressure and hence flow, both by its resistance and by the turbulence it creates.

Figure 7 is a schematic of the human circulatory system, showing average blood pressures in its major parts for an adult at rest. The left ventricle increases arterial blood pressure that drives the flow of blood through all parts of the body except the lungs.

The right ventricle receives the lower pressure blood from two major veins and pumps it through the lungs for gas exchange with atmospheric gases — the disposal of carbon dioxide from the blood and the replenishment of oxygen.

Only one major organ is shown schematically, with typical branching of arteries to ever smaller vessels, the smallest of which are the capillaries, and rejoining of small veins into larger ones.

Similar branching takes place in a variety of organs in the body, and the circulatory system has considerable flexibility in flow regulation to these organs by the dilation and constriction of the arteries leading to them and the capillaries within them. The sensitivity of flow to tube radius makes this flexibility possible over a large range of flow rates.

Figure 7. Schematic of the circulatory system. Pressure difference is created by the two pumps in the heart and is reduced by resistance in the vessels. Branching of vessels into capillaries allows blood to reach individual cells and exchange substances, such as oxygen and waste products, with them.

The system has an impressive ability to regulate flow to individual organs, accomplished largely by varying vessel diameters. Each branching of larger vessels into smaller vessels increases the total cross-sectional area of the tubes through which the blood flows. For example, an artery with a cross section of 1 cm 2 may branch into 20 smaller arteries, each with cross sections of 0. In that manner, the resistance of the branchings is reduced so that pressure is not entirely lost.

This reduced velocity allows the blood to exchange substances with the cells in the capillaries and alveoli in particular. Explain why the viscosity of a liquid decreases with temperature—that is, how might increased temperature reduce the effects of cohesive forces in a liquid? Also explain why the viscosity of a gas increases with temperature—that is, how does increased gas temperature create more collisions between atoms and molecules?

When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why. Plumbing usually includes air-filled tubes near water faucets, as shown in Figure 8.

Explain why they are needed and how they work. Figure 8. The vertical tube near the water tap remains full of air and serves a useful purpose. What force is needed to pull one microscope slide over another at a speed of 1. A glucose solution being administered with an IV has a flow rate of 4. What will the new flow rate be if the glucose is replaced by whole blood having the same density but a viscosity 2.

All other factors remain constant. The pressure drop along a length of artery is Pa, the radius is 10 mm, and the flow is laminar. A small artery has a length of 1. If the pressure drop across the artery is 1. To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate for the following changes with all other factors remaining the same as in the original conditions. The arterioles small arteries leading to an organ, constrict in order to decrease flow to the organ.

To shut down an organ, blood flow is reduced naturally to 1. By what factor did the radii of the arterioles constrict? Penguins do this when they stand on ice to reduce the blood flow to their feet. Angioplasty is a technique in which arteries partially blocked with plaque are dilated to increase blood flow. By what factor must the radius of an artery be increased in order to increase blood flow by a factor of 10?

By what factor must the pressure difference increase? A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. Show that the terminal speed is given by. Using the equation of the previous problem, find the viscosity of motor oil in which a steel ball of radius 0.

The densities of the ball and the oil are 7. A skydiver will reach a terminal velocity when the air drag equals their weight. For a skydiver with high speed and a large body, turbulence is a factor. The drag force then is approximately proportional to the square of the velocity.

A layer of oil 1. Researchers find that a force of 5. What type of oil might it be? Example 1 above dealt with the flow of saline solution in an IV system.

This reversal can be a problem when patients stand up. When physicians diagnose arterial blockages, they quote the reduction in flow rate. To those who agreed with him, Bush pledged that the law against same-sex marriage would remain intact. In Israel, however, a new law took effect January 1st that banned the use of underweight models. We should have to admit that the new law does little or nothing to relieve such a situation.

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Now this setting up of an orderly law-abiding self seems to me to imply that there are impulses which make for order. These schools became affiliated Universities, but never equalled the Law University in importance. Poiseuille's law. New Word List Word List. Save This Word! We could talk until we're blue in the face about this quiz on words for the color "blue," but we think you should take the quiz and find out if you're a whiz at these colorful terms.