MCAT Physics: Fluids
Conversions between Pa, mmHg, torr, and atm
1 atm = 760 mmHg = 760 torr = 1.013*10^5 Pa
A patient needs an injection of meds at least 109.3 kPa at injection site before surgery. If lying on a bed 0.9m high, what is the min height above the ground that the nurse must suspend the bag to achieve that pressure at injection site? Density of fluid = 1020 kg/m^3
1.7 m above ground Use hydrostatic pressure formula: P = Patm + gh 109.3 kPa = absolute pressure (P) 109.3 kPa = 101.3 kPa + (10m/s^2)(h) 0.8 m = h Height above ground = 0.8m + 0.9m = 1.7m
What's resistance proportional to?
1/r^4
What is atmospheric pressure
100,000 Pa
How many liters are in a cubic meter?
1000
Density of water
1000 kg/m^3 = 1 g/cm^3
A 5 m^3 object is sinking in water. It has an apparent weight of 16N. What is the object's density?
1000.32 kg/m^3
Atmospheric pressure in Pa?
101,000 Pa = 101 kPa
If the density of Ketchup is 1400 kg/m^3, what's its specific gravity?
1400/1000 = 1.4 No units
If radius cuts in 1/2, how much does resistance increase?
16 times more resistance. This is because in Pouseille's law, r^4 is in the denominator
Water flows from a pipe of diameter 0.15m into one of diameter 0.2m. If the speed in the 0.15m pipe is 4.88 m/s, what is the speed in the 0.2m pipe?
2.7 m/s
If specific gravity is 0.2, how much of the object will be submerged?
20% submerged. The rest above water
What's a typical gauge pressure for a tire
207 Pa or 30 psi
If the density of an object is 2700 kg/m^3, how much of the object will be submerged?
2700/1000 = 2.7 specific gravity 270% submerged = 100% submerged
Two wooden balls of equal volume but different density are held beneath the surface of a container of water. Ball A has a density of 0.5 g/cm^3, and ball B has a density of 0.7 g/cm^3. When they're released, they will accelerate up to the surface. What's the relationship between acceleration of A and that of B? A. Ball A has the greater acceleration B. Ball B has the greater acceleration C. They have the same acceleration D. It cannot be determined
A. Ball A has the greater acceleration Both balls experience the same buoyant force bc they are in the same liquid and have the same volume. Thus, the ball with the smaller mass experiences greater acceleration: Fbuoy = rho*V*g And, mass = rho*V
When the gauge pressure is doubled, what happens to the absolute pressure? A. It is halved B. It increases by a factor less than 2 C. If stays the same D. It doubles
B. It increases by a factor less than 2
A gold crown recently acquired is suspected to be brass covered in gold. The crown weighs 25.0N in air and has an apparent weight of 22.5N in fresh water. Based on these results, which of the following conclusions is correct? Density of gold = 19,300kg/m^3, density of brass = 8300-8700 kg/m^3 A. The crown is made of brass only B. It is made of brass covered in gold C. It is made of gold only D. It is made of half brass and half gold
B. It's made of brass covered in gold
There is a 2 liter container filled with with 500ml of h2o placed on top of a scale displaying 80 lbs. When a metal cube is submerged tied to a string end into the container, which of the following statements accurately describes the result? A. The cube's density must be provided to predict what will happen B. The scale will register a weight greater than 80 lbs due to Newton's third law C. The scale will remain at 80 lbs until the cube is floating on top of the water fully submerged D. The scale will remain at 80 lbs unless the cube touches the bottom of the bowl
B. The scale will register a weight greater than 80 lbs due to Newton's third law This is because there is a buoyant force keeping the objec afloat pushing upward, and an equal and opposite force downwards. This additional force causes the scale to register a weight greater than 80 lbs
According to the Poiseuille's Law, which of the following statements correctly describes blood flow through arteries? A. If the original flow rate is 100 cm3/sec, doubling the radius will increase the flow rate to 800 cm^3/sec B. Vasoconstriction by 20% will reduce the blood flow rate by a factor of 8. C. Vasodilation by 20% will double the blood flow rate. D. Resistance is proportional to the radius to the fourth and inversely proportional to flow rate.
C. Vasodilation by 20% will double the blood flow rate. core equations: Q = ΔP/R, R =8ηL/πr^4 so. Q=ΔPπr^4/η8L. Volume flow rate (Q) is proportional to the radius raised to the fourth. Vasoconstriction by 20% can expressed as 0.8. Its effect on the blood flow rate is (0.8)^4, which is 0.4. To reduce the blood flow rate by a factor of 8 would mean 0.125. If the original flow rate is 100 cm^3/sec, doubling the radius will increase the flow rate to 1600 cm/sec since 2^4 = 16. Resistance is inversely proportional to the radius to the fourth and also to volume flow rate. Vasodilation by 20% can be expressed as 1.2. It's effect on blood flow rate would be (1.2)^4, which is approx 2.0
Objects A and B are submerged at depth of 1m in a liquid with a specific gravity of 0.877. Given that the density of object B is 1/3 that of object A and that the gauge pressure of object A is 3atm, what is the gauge pressure of object B? A. 1atm B. 2atm C. 3atm D. 9atm
C. 3 atm The absolute gauge pressures depend only on the density of the fluid, not that of the object. When the pressure at the surface is equal to atmospheric pressure, the gauge pressure is given by Pgauge = rho*g*z Rho represents the density of the fluid, not the object. The objects are also at the same depth, so they must have the same gauge pressure
Which of the following expressions is representative of total power output? (Q = volumetric flow rate, P = pressure) A. (P⋅t)/Q B. P · V · t C. P · Q D. (P⋅Q)/t
C. P · Q PQ would be the same as multiplying by volume and dividing by time.
According the the Bernoulli principle and continuity eqn, which of the following accurately describes the phenomenon of vascular flutter which occurs when an artery becomes constricted due to accumulated plaque in its inner walls? A. Constriction in the blood vessel causes the pressure to build up right at the narrowing B. The constriction will cause the blood to flow faster and the extra blood will create pressure after the narrowing C. The construction causes the pressure to drop and the vessel to collapse D. Construction in the blood vessel causes backup and the reassure to build before the narrowing
C. The construction causes the pressure to drop and the vessel to collapse Vascular flutter occurs when plaque accumulates and constricts and artery, and due to constriction, blood flows faster through the narrowing. Continuity eqn. Bernoulli tells us that that faster the fluid travels, the less the pressure of that fluid at that same point. Thus, if rate is sufficiently high, the artery will collapse at the region of plaque and stop blood flow temporarily
What gives rise to surface tension
Cohesion: attractive force molecules feel toward other molecules of the same liquid
Blood takes about 1.0 seconds to pass through a 1.0 millimeter long capillary in the human circulatory system. If the diameter of the capillary is 8.00 μm and the pressure drop is 2.0 kPa, what is the viscosity of the blood, assuming laminar flow? A. 40 μPa·s B. 40 mPa·s C. 4 μPa·s D. 4 mPa·s
D. 4 mPa·s
A tank with height y is filled with water to the top and is placed at a height z above the ground. Currently the water level is 3 meters above the ground. At the bottom of the tank, there is a hole where the water can flow out when needed. Which of the following would increase the flow rate? A. Increase y and z without adding additional water B. Decrease the size of the hole to increase the velocity out of the hole C. Increase z D. Increase the size of the hole
D. Increase the size of the hole Decreasing the size of the hole is reminiscent of he continuity eqn. However, the eqn implies conservation of mass, so more volume would not come through
According to Bernoulli and Venturi, if the water flows faster, the pressure _______________
Decreases
What is the pressure of a liquid?
Density*height*gravity
How to find force imposed by coefficient of viscosity
F = ñ*A (v/d)
What do raindrops look like as they fall through earth's atmosphere?
In deciding on the shape of the raindrop, there are two forces at play here: the surface tension holding the droplet together and the air pressure pushing from below against the bottom surface of the droplet. Spherical is the most ideal shape achieved by surface tension to minimize surface area, but that shape is maintained for only small droplets. While teardrop-shaped is the shape promoted by popular culture and used in weather Being used as a popular icon does not make it wrong. forecasts, small raindrops will be spherical due to surface tension.
How can a simple hydraulic machine increase its output force relative to input force? Use external pressure
Initial Pressure = Final Pressure Force1/Area1 = Force2/Area2 thus, increasing area increases force.
How does pressure or depth impact buoyant force?
It doesn't - it is independent of surrounding pressure
Is pressure a scalar or a vector?
It is a scalar. It does not have direction
What is the buoyant force upward against the submerged object?
It is equal to the mass of the displaced fluid = (density of fluid)(volume of object that is submerged)
With is the difference between the upward and downward pressure or force on an object in a liquid
It is the same
How does an increase in pressure impact the boiling point of water in food?
It raises the boiling point, reducing cooking time and preventing loss of moisture. Increase BP. The increased pressure prevents the water molecules from escaping the liquid at the normal temperature. Need more energy, higher temps, for the water to boil. Hotter water, faster cooking time.
What effect does turbulence have on the energy of the system?
It significantly dissipates energy from the system as the result of increased frictional forces.
Flow rate =
Linear speed * cross sectional area
If an object is at rest halfway Submerged, what is its buoyant force?
Mass * gravity = volume*density*gravity
What is density?
Mass per volume: kg/m^3
What is the downward force of a liquid?
Mass*gravity = density*volume*gravity
A force is applied to a hydraulic lift over a distance of 3.6 m to lift a car of weight 1500N a distance of 1m. What is the magnitude of this force if the friction force exerted on the fluid by the walls of the container is 0.65 N/m^2?
More information is needed. Two problems: 1. Friction force means that this is non conservative, so we cannot apply pascals principle 2. Friction force is given as N/m^2. We don't know the dimensions of the container, thus we don't know how many newtons of frictional force are exerted on the fluid
Is there more pressure on the bottom or the top of the cube?
More on the bottom. This is what makes things float
What are Pascals?
N/m^2
Difference between coefficient of viscosity for a Newtonian vs non-Newtonian fluid
Newtonian fluid: ñ does not depend on speed with which you pull an object by it It stays the same regardless of other forces
As a sub dives deeper into the water, how much more strongly does its propellor have to propel it to greater depths?
No more strongly - buoyant force is independent of surrounding pressure
Does bernoulli's equation consider viscosity?
No! It assumes viscosity is negligible. Bernoulli's is an expression of energy conservation for flowing fluids
Can Bernoulli's be applied to turbulent flow systems?
No: energy cannot be conserved. All bernoulli's questions on the mcat will assume laminar flow
Bernoulli eqn
P1 + p v1^2 / 2 = P2 + p v2^2 / 2 Reference https://www.physicsforums.com/threads/fluid-velocity-and-flow-rate-questions.505325/
What does critical speed depend upon
Physical properties of the fluid: viscosity and diameter of tube
What is gauge pressure
Pressure of the system - atmospheric pressure
What is laminar flow?
Smooth, orderly layers of fluid flowing parallel to each other. They don't necessarily have the same linear speed, as layers closest to pipe wall flow more slowly than the interior layers But the different flow layers must be parallel and not cross
What is an objects apparent weight?
The net downward force on an object in a liquid
What is specific gravity?
The ratio of how dense a specific mater is to the density of water
Pouisseille's law (don't need to know the equation, just what it tells us)
The volume that flows through a pipe per time
When is Reynolds number used?
Used to determine critical speed - first speed at which pouisseille's law will not give an accurate answer
What is a non conservative force related to fluid dynamics
Viscosity. It's like air resistance in this way: higher viscosity increases its viscous drag More viscous fluids will lose energy while flowing
How do we determine buoyant force of given an object's density and weight in newtons?
Volume of the object must be determined, bc this equals the volume of the water displaced. Volume = mass / density Mass = weight / g Ex: a 833N object is 83.3kg If it's density is 7800 kg/m^2, it's volume is 83.3/7800
What is the buoyant force equal to?
Volume of water displaced * density of fluid * gravity
What is the net force upon a cube immersed in water?
Weight of liquid displaced * gravity
When does turbulence arise in fluid flow?
When speed exceeds the critical speed of the fluid
What is absolute pressure
atmospheric pressure plus gauge lressure
What eqn relates pressure to flow to resistance? This finds the total resistance in a system
deltaP = Q*R
If balsa wood has a density of 130 kg/m^3, how much of it is submerged in water?
volume submerged / total volume = density of balsa wood / density of water = 130/1000 = 13%
Coefficient of viscosity
Ñ
