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Ch 20: Fluid MechanicsWorksheetSee all chapters
All Chapters
Ch 01: Intro to Physics; Units
Ch 02: 1D Motion / Kinematics
Ch 03: Vectors
Ch 04: 2D Kinematics
Ch 05: Projectile Motion
Ch 06: Intro to Forces (Dynamics)
Ch 07: Friction, Inclines, Systems
Ch 08: Centripetal Forces & Gravitation
Ch 09: Work & Energy
Ch 10: Conservation of Energy
Ch 11: Momentum & Impulse
Ch 12: Rotational Kinematics
Ch 13: Rotational Inertia & Energy
Ch 14: Torque & Rotational Dynamics
Ch 15: Rotational Equilibrium
Ch 16: Angular Momentum
Ch 17: Periodic Motion
Ch 19: Waves & Sound
Ch 20: Fluid Mechanics
Ch 21: Heat and Temperature
Ch 22: Kinetic Theory of Ideal Gases
Ch 23: The First Law of Thermodynamics
Ch 24: The Second Law of Thermodynamics
Ch 25: Electric Force & Field; Gauss' Law
Ch 26: Electric Potential
Ch 27: Capacitors & Dielectrics
Ch 28: Resistors & DC Circuits
Ch 29: Magnetic Fields and Forces
Ch 30: Sources of Magnetic Field
Ch 31: Induction and Inductance
Ch 32: Alternating Current
Ch 33: Electromagnetic Waves
Ch 34: Geometric Optics
Ch 35: Wave Optics
Ch 37: Special Relativity
Ch 38: Particle-Wave Duality
Ch 39: Atomic Structure
Ch 40: Nuclear Physics
Ch 41: Quantum Mechanics
Intro to Pressure
Pascal's Law & Hydraulic Lift
Pressure Gauge: Barometer
Pressure Gauge: Manometer
Pressure Gauge: U-shaped Tube
Buoyancy & Buoyant Force
Ideal vs Real Fluids
Fluid Flow & Continuity Equation

Concept #1: Fluid Speed vs. Volume Flow Rate

Concept #2: Flow Continuity

Example #1: Continuity / Proportional Reasoning


Hey guys. So, in this example I want to quickly show how to deal with proportional reasoning or proportional change questions involving continuity, let's check it out. Alright, so here, we have water flow in a horizontal cylindrical pipe, something like this and it says, water has a speed of V at Point A. So, let's say that this is point A and at this point speed at A will be big V and point B has double the diameter. So, somewhere over here this thing grows to have double the diameter, right? So, point B is somewhere over here, B and the diameter, let's say that the diameter of A will be D and diameter of B will be twice that to D and we want to know what is the volume, what is the the velocity, the speed of water at this point, okay? And first I want you to think about this in conceptual terms, do you think the water will be faster or slower here? And hopefully you pick that the air the D water will be slower, remember, if water is going into a tighter pipe part or a tighter segment of the pipe it's going to go faster. So, if it's going to a wider section it's going to go slower and that's because water or fluid flow rates Q which equals A times speed is a constant. So, if the area increases which it does here the speed has decreased so that the products A V stays the same, okay?

So, one way to think about, this is, this is a 2 and this is a 10, right? And this grows to a 4, this is 20, this has to decrease to a 5 so that this is still 20, cool? So, it should be slower which means it, it's not going to be the same, it's not going to be faster. So, it's now down to whether it's V over 4 or V over 2 and what you can do is you can just write, you can write A1, V1 equals A2 V2, right? And we're solving for or I guess I could say a, a and a B, right? And we're writing, we're solving for VB. So, VB is the first area times the first speed divided by the second area. Now, the area of a cylindrical pipe is pi, r squared. So, I can write pi, r square divided by pi, r squared times the first velocity which is V, okay? Now, I don't have the radius, I have the, I have the the diameter but diameter is half the radius and if the diameter is doubling that means that the radius doubles as well. So, I can simplify this whole thing by saying, I'm just going to call this r and this is going to be 2r, okay? So, if the diameter doubles the radius doubles and all these questions whenever you have diameter, pretty much in all of physics whenever you see diameters are supposed to change that into radius, okay? So, one is double the other so the pi's will cancel and I can say that A is r and then this guy here is 2r times V. So, look what happens, I have, I have r square, this 2 here becomes a 4, 4r squared so the rs squares cancel and you're left with V over 4, okay? So, if the radius becomes twice as big then the speed will become 4 times smaller and that's because the area depends on the square of the radius. So, if the radius becomes twice as big then the area becomes 4 times greater which means that the speed has to go down by a factor of 4 so the answer will be V over 4, cool? These are pretty popular, hopefully this makes sense, let's keep going.