Physics Exam 1
During a marathon race, a runner's blood volume flow rate increases to 10.0 times her resting rate. Her blood's viscosity has dropped to 95.0% of its normal value due to an increase in core temperature, and the blood pressure difference across her circulatory system has increased by 50.0%. By what factor has the average radius of her blood vessels increased?
1.6
Water flows into a horizontal, cylindrical pipe at 1.6 m/s. The pipe then narrows until its diameter is halved. What is the pressure difference between the wide and narrow ends of the pipe?
1.9×10^4 Pa
A 1.0 μm long bacterium swims through water at 10 μm/s. Water has a density of 1000 kg/m3 and a viscosity of 1.0 centipoise. Calculate the Reynolds number for the bacterium.
10^-5
The Antarctic krill (Euphausia superba) has a length of 6.0 cm and has a maximum speed of 0.8 m/s. What is the Reynold's number of a krill moving through 20˚C water? Do intertial or viscous forces dominate for a krill moving at its maximum speed?
10^4; inertial
A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline. What is the density of the block if the density of water is 1.00 g/cm^3?
.50 g/cm^3
The viscosity of blood at normal hematocrit is about 4.75 mPa-s, compared to the viscosity of water, which is 1 mPa-s. In an adult human the coronary arteries have a diameter of about 4 mm. Suppose you are able to produce a flow rate Q of water in a tube that is the same diameter as the coronary artery. If you wanted to produce this same flow rate using blood, what would the diameter of the tube have to be (assuming all other variables are held constant)?
5.9 mm
A spherical object of diameter 0.5 m is immersed in a fluid. It experiences a pull downwards by gravity and a push upwards by buoyancy. If the object is denser than the fluid, it will accelerate downwards and experience a viscous force upwards proportional to its speed. Eventually, the upward and downward forces will balance each other out and the object will move at a constant "terminal" speed. Assume the mass of the object is 80 kg; the density of the fluid is 1000 kg/m^3 and its viscosity is 200 Pa.s. A) What is the density of the sphere? B) What is the terminal velocity of the sphere in the fluid? C) The same object as above is now moving in a different fluid whose density is also 1000 kg/m^3 but whose viscosity is unknown. However, experiments show that the terminal velocity is 0.01m/s. What is the viscosity of this unknown fluid?
A) 1222.3 kg/m^3 B) 0.15 m/s C) 3013 Pa*S
A drug of viscosity 8.9 x 10^-4 Pa-s is being delivered into a patient's arm at a rate of 10 mL/min through a syringe with a 5cm long needle. The needle's internal diameter is 1 mm. Assume the patient's blood gauge pressure is 110 mmHg. A) What must be the gauge pressure in kPa in the body of the syringe be? B) What is the drug's volume flow rate?
A) 15.3 kPa B) 1.67 x 10^-7
Block A is released from rest at the center of a tank of water. The block accelerates upward. When block A reaches the surface, it is observed to float at rest. A) In this final position, is the buoyant force on block A greater than, less than, or equal to its weight? B) If 90% of block A lies below the surface of the water in its final position, then how does the density of block A compare to the density of water? C) This block is then released in fluid 2x as dense as water. What will happen to it?
A) There is no net force accelerating the block since it is at rest, so the forces are equal B) The density is 90% the density of water C) It will go to the surface with 2x the acceleration
A fluid is flowing through tube 1 at speed v1. Tube 1 has a cross sectional area A1. Tube 1 splits into 2-4, which all have the same cross sectional area A. The twater flows through each of these tubes at the same speed, v. What is the equation of continuity for this system?
A1v1=v(A+A+A)
A bacterium has a Reynolds number of 10^-5. What types of forces dominate, and how will it stop when it stops swimming?
For the bacterium, viscous forces dominate, so when it ceases swimming it comes to a halt immediately because drag/viscous forces oppose motion in a fluid
What does the Venturi meter do?
It uses the difference in pressure between two points in a pipe of varying cross section to measure the flow speed of a fluid.
If an ideal fluid element flows from a lower to a higher elevation, what happens to its energy?
Its potential energy increases, its kinetic energy decreases, and its total mechanical energy remains the same.
A ball of mass mb and volume V is lowered on a string into a fluid of density ρf. Assume that the object would sink to the bottom if it were not supported by the string. What is the tension T in the string when the ball is fully submerged but not touching the bottom? Express your answer in terms of any or all of the given quantities and g, the magnitude of the acceleration due to gravity.
T = (mbg)−(gρfV)
What is the Reynold's number?
The Reynolds number (Re) is the ratio of the inertial to the viscous (drag) forces acting on an object moving through a fluid.
Is the Reynolds number a property of a fluid, of an object, or of an object moving in a fluid?
The Reynolds number is a property of an object moving in a fluid; it depends on the dimensions of the object and its motion as well as on the fluid.
If an ideal fluid element moves from a region of lower pressure to a region of higher pressure, is the work done on it by the pressure force positive, negative, or zero?
negative (moving from a lower to higher pressure causes the fluid to slow down, removing KE from the system, so negative work has been done)
What is Archimedes' Principle?
the magnitude of the buoyant force equals the weight of the fluid displaced by the object
When the Reynolds number is small, ______________ forces dominate.
viscous
A 30 m long blue whale swims through water at 10 m/s. Water has a density of 1000 kg/m3 and a viscosity of 1.0 centipoise. What is its Reynolds number?
3 x 10^8
What is a drag force?
A force that acts to oppose the relative motion of an object in a fluid
A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline. The wooden block is removed from the water bath and placed in an unknown liquid. In this liquid, only one-third of the wooden block is submerged. What is the density of the unknown liquid?
1.5 g/cm^3
The leaves of a tree lose water to the atmosphere via the process of transpiration. A particular tree loses water at the rate of 3×10^−8m^3/s; this water is replenished by the upward flow of sap through vessels in the trunk. This tree's trunk contains about 2000 vessels, each 100 μm in diameter. What is the speed of the sap flowing in the vessels?
0.002 m/s
River Pascal with a volume flow rate of 7.0×10^5 L/s joins with River Archimedes, which carries 1.06×10^6 L/s , to form the Bernoulli River. The Bernoulli River is 140 m wide and 30 m deep. What is the speed of the water in the Bernoulli River?
0.42 m/s (1 L = 0.001 cubic meters)
Smoking tobacco is bad for your circulatory health. In an attempt to maintain the blood's capacity to deliver oxygen, the body increases its red blood cell production, and this increases the viscosity of the blood. In addition, nicotine from tobacco causes arteries to constrict. For a nonsmoker, with blood viscosity of 2.5×10^−3Pa⋅s, normal blood flow requires a pressure difference of 8.0 mm of Hg between the two ends of an artery. If this person were to smoke regularly, his blood viscosity would increase to 2.7×10^−3Pa⋅s, and the arterial diameter would constrict to 90 % of its normal value. What pressure difference would be needed to maintain the same blood flow in mm Hg?
13 mm of Hg
What pressure difference is required between the ends of a 2.0-m-long, 1.0-mm-diameter horizontal tube for 40∘C water to flow through it at an average speed of 4.0 m/s?
179200 Pa
A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline. Masses are then stacked on top of the block until the top of the block is level with the waterline. This requires 20 g of mass. What is the mass of the wooden block?
20g (With the 20g mass on the block, 2x as much of the block is underwater, therefore the buoyant force doubles. If the buoyant force doubled, then so did the weight force because the object is still floating)
A 0.3 mm long invertebrate larva moves through 20˚C water at 1.0 mm/s. You are creating an enlarged physical model of this larva so you can better study its flow pattern in the laboratory. Your model must be able to move at 50 cm/s and you will place the model in honey instead of water. Honey has a density of 1400 kg/m^3 and a viscosity of 600 Pa-s. How long should your model be?
25.7 cm
A viscous fluid flows through a tube at an average speed of Vavg. If the pressure difference doubles, but the diameter is unchanged, what would be the new average speed of the fluid?
2Vavg
Water flowing through a 1.9-cm-diameter pipe can fill a 500 L bathtub in 7.0 min . What is the speed of the water in the pipe?
4.2 m/s
An airfoil is the shape of an airplane wing. You are designing a plane that is supposed to fly at 100 m/s. The airfoil has a length of 2.5 m. Air has a density of 1.2 kg/m^3 and a viscosity of 0.018 centipoise. At what speed would a 1/40th scale model of the plane have to fly in order to reproduce the flow pattern of air around the airfoil of the real airplane? Explain/show your work.
4000 m/s (The flow of a fluid around an object can be studied by making a scale model of the object In order to make sure that the flow patterns around the model and the real object are the same, their Reynolds numbers must match.)
A viscous fluid flows through a tube at an average speed of Vavg. If the tube's diameter doubles, but the pressure difference between the ends of the tubes is unchanged, what would be the new average speed of the fluid?
4Vavg
Carotid arteries on either side of the neck feed blood to the brain. A patient's carotid arteries are 11.2 cm long and have an inner diameter of 5.2 mm. Near the middle of the left artery is a stenosis where the diameter narrows to 3.4 mm. If the volume flow rate in the 2 arteries is the same, what is the ratio of the pressure drop along the stenosis in the left artery to the pressure drop along the corresponding segment in the right artery?
5.47
The aorta has cross-sectional area of 3.0 cm^2. Blood moves through the aorta at 30 cm/s. A capullary has a cross-sectional area of 2.8 x 10^-7 cm^2, and blood moves through a capillary at 0.05 cm/s. Estimate the number of capillaries in the body.
6.4 x 10^9
The average density of the body of a fish is 1080 kg/m^3. To keep from sinking, the fish increases its volume by inflating an internal air bladder, known as a swim bladder, with air. By what percent must the fish increase its volume to be neutrally buoyant in fresh water? Use 1.28 kg/m^3 for the density of air at 20˚C
8%
A viscous fluid flows down a long tube. At the tubes midpoint the diameter suddenly triples. The pressure difference between the tube's entrance and midpoint is 800 Pa. What is the pressure difference between the midpoint of the tube and the exit?
9.9 Pa
Object A and object B are identical, except object A is moving very fast while object B is moving very slow. Object __ requires the greater force in order to come to rest in the same period of time.
A
The blood pressure at your heart is approximately 100 mm of Hg. As blood is pumped from the left ventricle of your heart, it flows through the aorta, a single large blood vessel with a diameter of about 2.5 cm. The speed of blood flow in the aorta is about 60 cm/s. Any change in pressure as blood flows in the aorta is due to the change in height: the vessel is large enough that viscous drag is not a major factor. As the blood moves through the circulatory system, it flows into successively smaller and smaller blood vessels until it reaches the capillaries. Blood flows in the capillaries at the much lower speed of approximately 0.7 mm/s. The diameter of capillaries and other small blood vessels is so small that viscous drag is a major factor. A) There is a limit to how long your neck can be. If your neck were too long, no blood would reach your brain! What is the maximum height a person's brain could be above his heart, given the noted pressure and assuming that there are no valves or supplementary pumping mechanisms in the neck? The density of blood is 1060 kg/m3 . B) Because the flow speed in your capillaries is much less than in the aorta, the total cross-section area of the capillaries considered together must be much larger than that of the aorta. Given the flow speeds noted, the total area of the capillaries considered together is equivalent to the cross-section area of a single vessel of approximately what diameter? C) Suppose that in response to some stimulus a small blood vessel narrows to 90 % its original diameter. If there is no change in the pressure across the vessel, what is the ratio of the new volume flow rate to the original flow rate? D) Sustained exercise can increase the blood flow rate of the heart by a factor of five with only a modest increase in blood pressure. This is a large change in flow. Although several factors come into play, which of the following physiological changes would most plausibly account for such a large increase in flow with a small change in pressure? A) A decrease in the viscosity of the blood. B) Dilation of the smaller blood vessels to larger diameters. C) Dilation of the aorta to larger diameter. D) An increase in the oxygen carried by the blood.
A) 1.3 m B) 73 cm C) .66 D) B) Dilation of the smaller blood vessels to larger diameters.
An "airfoil" is the term used to describe the cross-sectional shape of a wing. Let's say you are designing a plane that is supposed to fly at 100 m/s and the airfoil has a length of 2.5 m. Assume air has a density of 1.2 kg/m and a viscosity of 0.018 centipoise. A) What is the Reynolds number for this situation? B) At what speed would a 1/40th scale model of the plane have to fly in order reproduce the flow pattern of air around the airfoil of the real plane?
A) 1.67 x 10^7 B) 4000 m/s
A cylindrical beaker of height 0.100 m and negligible weight is filled to the brim with a fluid of density ρ = 890 kg/m^3 . When the beaker is placed on a scale, its weight is measured to be 1.00 N. A ball of density 5000 kg/m^3 and volume V = 60.0 cm^3 is then submerged in the fluid, so that some of the fluid spills over the side of the beaker. The ball is held in place by a stiff rod of negligible volume and weight. A) What is the weight of the ball? B) What is the reading of the scale when the ball is held in this submerged position? Assume that none of the water that spills over stays on the scale. C) What is the force applied to the ball by the rod? D) The rod is now shortened and attached to the bottom of the beaker. The beaker is again filled with fluid, the ball is submerged and attached to the rod, and the beaker with fluid and submerged ball is placed on the scale. What weight does the scale show now?
A) 2.94 N B) 1 N (The "extra force" that the ball exerts on the water is equal to the force that the water exerts on the ball, that is, the weight of the displaced water. Therefore, the reading does not change.) C) 2.42 N D) 3.42 N
A) For an object of radius 0.25m moving in honey at 70F (viscosity 20 Pa.s), what is the drag force at a speed of 0.1 m/s? B) If the object is moving horizontally and at the same constant speed of 0.1 m/s, a force must be exerted on it to maintain that motion. That means someone is doing work! Calculate the work required to maintain the motion for 16 seconds. C) Compute the Reynolds number assuming the density of the fluid is 1.36kg/m^3. Is the flow likely to be laminar (as assumed above) or turbulent?
A) 9.42 N B) 15.07 J C) Laminar
Ice at 0.0˚C has a density of 917 kg/m^3. A 3.00 cm^3 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. A) What is the density of the oil? B) Once the ice cube melts, what happens to the liquid water that it produces? C) What happens if some ethyl alcohol of density 790 kg/m^3 is poured into the container after the ice cube has melted?
A) 917 kg/m^3 B) The liquid water sinks to the bottom of the container since it is more dense C) The layer of ethyl alcohol forms on the surface.
A flask of water rests on a scale that reads 100 N. Then, a small block of unknown material is held completely submerged in the water. The block does not touch any part of the flask, and the person holding the block will not tell you whether the block is being pulled up (keeping it from falling further) or pushed down (keeping it from bobbing back up). Assume that no water spills out of the flask. A) What is the new reading on the scale? B) The experiment is repeated with 6 differnent blocks: A has a mass of 100g and 50cm^3 volume, B is 100g and 200cm^3, C is 200g and 50cm^3, D is 50g and 100cm^3, E is 200g and 100cm^3, and F is 400g and 50cm^3. Rank these blocks on the basis of the scale reading when the blocks are completely submerged. C) If the blocks were released while submerged, which, if any, would sink to the bottom of the flask?
A) Greater than 100N B) B > D=E > A=F=C C) A, C, E, and F
Organism A swims through 20˚C water at a speed v, creating a particular flow pattern. Organism B moves through air at the same speed v and creates an identical flow pattern. Air has a density of 1.2 kg/m3 and a viscosity of 0.018 centipoise. A) Which organism must be larger? B) How many times larger is the larger organism compared to the smaller organism?
A) Organism B B) 15x
Object A and object B move at the same speed, but object B is more massive than object A. Object __ requires the greater force in order to come to rest in the same period of time.
B
The aorta has cross-sectional area of 3.0 cm^2. Blood moves through the aorta at 30 cm/s. A capullary has a cross-sectional area of 2.8 x 10^-7 cm^2, and blood moves through a capillary at 0.05 cm/s. Which of the following must be true? A) The aorta's cross sectional area must be greater than the sum of all the cross-sectioanl areas of all of the capillaries in the body B) The aorta's cross sectional area must be equal to the sum of all the cross-sectioanl areas of all of the capillaries in the body C) The aorta's cross sectional area must be less than the sum of all the cross-sectioanl areas of all of the capillaries in the body
C) The aorta's cross sectional area must be less than the sum of all the cross-sectioanl areas of all of the capillaries in the body
A section of the artery increased its diameter by 5% (due to an aneurism), would the pressure difference across that section of artery increase or decrease, and by how much?
Decreased by 18%
A whale has a Reynolds number of 3x10^8. What types of forces dominate, and how will it stop when it stops swimming?
For the whale, inertial forces dominate, so when it ceases swimming it will coast to a stop.
Block A is released from rest at the center of a tank of water. The block accelerates upward. At the instant the block is released, is the magnitude of the buoyant force on block A greater than, less than, or equal to the magnitude of its weight?
If the block accelerates upward, there must be a net upward force, so the buoyant force is greater than the weight force
King Hiero II suspected that his gold crown was not pure gold (ρgold = 19,300 kg/m^3). He asked Archimedes to determine if the crown was pure gold without damaging the crown. Archimedes suspended the crown by a rope in a tank of water (ρwater = 1000 kg/m^3). The tension in the rope was 30 N. The crown's volume was 0.0002 m^3. Was the crown made of pure gold?
No
If the radius of an artery is decreased by 5% but the pressure difference between its two ends is not changed, what will happen to the volume flow rate of the blood in the artery?
Qnew=0.81Qold
A balloon is partially inflated and sealed. A number of weights are attached to the balloon such that it is neutrally buoyant when submerged at a certain depth in a beaker of water. Describe the motion of the balloon, if you push the balloon down to a greater depth and release it. Explain.
The pressure will be larger at the greater depth. Since the balloon is only partially inflated, its volume will therefore shrink and the buoyant force on it will decrease. Since its weight remains the same, the buoyant force will no longer be large enough to balance its weight and the balloon will sink.
A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline. What is the buoyant force acting on the block?
W (If it is floating and not moving, the buoyant force must equal the weight force of the object since F=ma, so m1g=m2g and ρ1V1g=ρ2V2g, but this does not mean that ρ1 has to equal ρ2, and V1 must equal V2, just as long as some combination of the two makes them equal)
A 2.0 mL syringe has an inner diameter of 4.5 mm , a needle inner diameter of 0.24 mm , and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100. Assume the liquid is an ideal fluid. a) What is the minimum force the nurse needs to apply to the syringe? b) The nurse empties the syringe in 2.8 s . What is the flow speed of the medicine through the needle?
a) 0.21 n b) 16 m/s
A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 0.5 cm. Liquid flows through the first segment at a speed of 4.0m/s. a) what is the speed in the 2nd segment? b) What is the speed in the 3rd segment? c) What is the volume flow rate through the pipe?
a) 1 m/s b) 16 m/s c) .31 L/s
Assume that the viscosity of blood is 2.8 x 10^−3 Pa-s. The pulmonary artery, which connects the heart to the lungs, is 8.5 cm long and has a pressure difference over this length of 450 Pa. a) If the inside radius of the artery is 2.4 mm, what is the volume of blood that flows per second through the pulmonary artery? b) If the radius of the artery is reduced by 12 % , by what factor is the blood flow rate reduced? Assume that all other properties of the artery remain unchanged.
a) 25 cm^3/s b) .60
A hurricane wind blows across a 5.00m×11.0m flat roof at a speed of 150 km/h . a) Is the air pressure above the roof higher or lower than the pressure inside the house? Explain. b) What is the pressure difference Δp=pinside−poutside? Use 1.28 kg/m^3 for the density of air. c) How much force is exerted on the roof? d) If the roof cannot withstand this much force, will it "blow in" or "blow out"?
a) The pressure above the roof is lower due to the higher velocity of the air. b) 1100 Pa c) 61000 n d) The roof will blow outward (up), because pressure inside the house is greater than pressure on the top of the roof.
Consider the following statement: The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true? a) for every object submerged partially or completely in a fluid b) for an object that floats c) for an object that sinks d) for no object submerged in a fluid
a) for every object submerged partially or completely in a fluid
Water enters a house at 1.5 m/s through a pipe with an inside radius of 1 cm and pressure of 400,000 Pa. The water travels 5m up to a second floor bathroom through a pipe of radius 0.5 cm. a) How does the speed of the water when it reaches the bathroom (v2) compare to its initial speed (v1)? b) Whatis the speed of water when it reaches the bathroom? c) What is the pressure in Pa of water when it reaches the bathroom>
a) v2=4v1 b) 6 m/s c) 334,125 Pa
Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true? a) Object T has a greater density than object B. b) Object B has a greater density than object T. c) Both objects have the same density.
b) Object B has a greater density than object T.
Consider the following statement: The magnitude of the buoyant force equals the weight of the object. Under what circumstances is this statement true? a) for every object submerged partially or completely in a fluid b) for an object that floats c) for an object that sinks d) for no object submerged in a fluid
b) for an object that floats
An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a denser liquid. What would you observe? a) The object would sink all the way to the bottom. b) The object would float submerged more deeply than in the first container. c) The object would float submerged less deeply than in the first container. d) More than one of these outcomes is possible.
c) The object would float submerged less deeply than in the first container.
Consider the following statement: The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object. Under what circumstances is this statement true? a) for an object that is partially submerged in a fluid b) only for an object that floats c) for an object completely submerged in a fluid d) for no object partially or completely submerged in a fluid
c) for an object completely submerged in a fluid
Consider the following statement: The magnitude of the buoyant force is less than the weight of the object. Under what circumstances is this statement true? a) for every object submerged partially or completely in a fluid b) for an object that floats c) for an object that sinks d) for no object submerged in a fluid
c) for an object that sinks
An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a less dense liquid. What would you observe? a) The object would sink all the way to the bottom. b) The object would float submerged more deeply than in the first container. c) The object would float submerged less deeply than in the first container. d) More than one of these outcomes is possible.
d) More than one of these outcomes is possible. (If the fluid in the second container is less dense than the object, then the object will sink all the way to the bottom. If the fluid in the second container is denser than the object (though less dense than the fluid in the original container), the object will still float, but its depth will be greater than it was in the original container)
An object is moving through a viscous fluid. If the speed of the object increases, then the magnitude of the drag force _________
increases
An object is moving through viscous fluid. If the size of the object increases, then the magnitude of the drag force ________-
increases
An object is moving through a viscous fluid. If the viscosity of the fluid increases, then the magnitude of the drag force _________-
increases.
When the Reynolds number is large, _____________forces dominate.
inertial
What type of forces acting on an object determine its Reynolds number?
inertial forces and drag forces
A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline. The wooden block is removed from the water bath and placed in an unknown liquid. In this liquid, only one-third of the wooden block is submerged. Is the unknown liquid more or less dense than water?
more dense
Severe anemia, in which the hematocrit of the blood is < 30%, can reduce the viscosity of the blood to 75% its normal value. If nothing else were to change, how would the pressure drop along the carotid artery in the anemic condition compare to the pressure drop in the normal condition?
∆Pa=0.75∆Pn