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. Sails also have the characteristic shape of a wing. See Figure 2 b. The pressure on the front side of the sail, P front , is lower than the pressure on the back of the sail, P back.
This results in a forward force and even allows you to sail into the wind. The manometer in Figure 3 a is connected to two tubes that are small enough not to appreciably disturb the flow. Figure 3. Figure 4 b shows a version of this device that is in common use for measuring various fluid velocities; such devices are frequently used as air speed indicators in aircraft. Figure 4. Tube 1 is open at the end facing the flow. A dead spot having zero speed is created there.
Tube 2 has an opening on the side, and so the fluid has a speed v across the opening; thus, pressure there drops. You can squirt water a considerably greater distance by placing your thumb over the end of a garden hose and then releasing, than by leaving it completely uncovered. Explain how this works. Water is shot nearly vertically upward in a decorative fountain and the stream is observed to broaden as it rises. Conversely, a stream of water falling straight down from a faucet narrows.
Explain why, and discuss whether surface tension enhances or reduces the effect in each case. Refer to Figure 1. Answer the following two questions.
Why is P o less than atmospheric? Why is P o greater than P i? Air passing between the vehicles flows in a narrower channel and must increase its speed v 2 is greater than v 1 , causing the pressure between them to drop P i is less than P o. Many entrainment devices have a constriction, called a Venturi, such as shown in Figure 5. How does this bolster entrainment? Figure 5. A tube with a narrow segment designed to enhance entrainment is called a Venturi.
These are very commonly used in carburetors and aspirators. Some chimney pipes have a T-shape, with a crosspiece on top that helps draw up gases whenever there is even a slight breeze. Is there a limit to the height to which an entrainment device can raise a fluid? Explain your answer. Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado.
It is dangerous to stand close to railroad tracks when a rapidly moving commuter train passes. Explain why atmospheric pressure would push you toward the moving train.
Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.
A perfume bottle or atomizer sprays a fluid that is in the bottle. Figure 6. How does the fluid rise up in the vertical tube in the bottle? Atomizer: perfume bottle with tube to carry perfume up through the bottle. If you lower the window on a car while moving, an empty plastic bag can sometimes fly out the window. Asked 3 years, 8 months ago. Active 14 days ago. Viewed 1k times. The volume flow rate is zero because there is no net force on the fluid II.
The volume flow rate is constant throughout the pipe because the cross-sectional area is uniform III. The pipe is not inclined relative to the horizontal since the pressure is constant.
Part of my question is when these relationships apply: Bernoulli's I can use when i have incompressible non viscous fluid. Improve this question. Urb 2, 4 4 gold badges 10 10 silver badges 25 25 bronze badges. Kevin Lee Kevin Lee 85 1 1 silver badge 5 5 bronze badges. Who told you that there is? A pressure differential is required to establish flow in a pipe.
If dP is zero, there is no "driving force" for fluid flow. Remember it's an inviscid fluid. If the fluid is flowing before it enters the pipe, there will be a pressure drop in the pipe due to fluid friction with the walls of the pipe. A pressure drop can't occur from the "fluid friction" if there is no viscosity.
Show 2 more comments. Active Oldest Votes. Improve this answer. It is dimensionally consistent with appropriate definition of R.
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