Good morning! This is my review of Unit 8, Fluids, for AP Physics 1. ♪ Flipping Physics ♪ This video is a free portion of my AP Physics 1 Ultimate Review Packet. If you are studying the AP Physics 1 curriculum this year, I absolutely recommend you also get my full AP Physics 1 Ultimate Review Packet. It’ll help you understand all this stuff. Link is in the video description, of course. Bo, please tell me the three most common states, or phases, of matter. Sure. Those would be solid, liquid, and gas. A solid has a fixed shape and fixed volume. A liquid does not have a fixed shape; however, a liquid does have a fixed volume. A gas does not have a fixed shape or a fixed volume. The term fluid means a substance which does not have a fixed shape. So, liquids and gasses are both fluids. Density equals mass divided by volume and the symbol we use for density is usually the lowercase Greek letter rho. Sure. But that is a lot more than what he asked for. Absolutely! Yep. Well done everybody. Please do the same thing for pressure. Okay. The general equation for pressure on a surface is pressure equals force perpendicular, or the component of the force perpendicular to the surface, divided by the area of the surface upon which it acts. Pressure is a scalar; therefore, it has magnitude but no direction. Typical units for pressure are pascals, capital P lowercase a, where one pascal equals one newton per square meter. The absolute pressure at a point in a fluid is the sum of the pressure at the top of the fluid, P sub naught, and the pressure caused by the weight of the vertical column of fluid above that point which is called gauge pressure. Right. Absolute pressure equals P naught plus rho g h, where rho g h is the gauge pressure, rho is the density of the fluid, g is the gravitational field strength, and h is the depth of the fluid. And remember gauge pressure does not depend on the cross-sectional area of the fluid causing the gauge pressure. Okay. Absolutely! Yep. Hold up. If I take a rectangular block that is resting on a table and rotate it so a smaller side of the block is in contact with the table, the weight of the block does not change, so the force causing the pressure from the block on the table stays the same, however, the contact surface area of the block with the table is decreased, so the pressure from the block on the table is now greater. But I thought you said pressure does not depend on area? I said gauge pressure does not depend on the cross-sectional area of the fluid causing the gauge pressure. You are talking about the pressure caused by the weight of an object on a surface, not the gauge pressure caused by a fluid. They are both pressure, however, those are two different things. Oh, right. Thanks. You are welcome. Well done everybody. Next up is the buoyant force. The buoyant force is the sum of all the forces applied by the fluid surrounding the object. The direction of the buoyant force from a fluid on an object is upward. And the buoyant force is equal in magnitude to the weight of the fluid displaced by the object. In other words, the buoyant force equals the mass of the fluid displaced by the object times the gravitational field strength. Because density equals mass divided by volume, we know the mass of the fluid displaced by the object equals density of the fluid displaced by the object times the volume of the fluid displaced by the object. Therefore, the buoyant force equals the density of the fluid displaced by the object times the volume of the fluid displaced by the object times gravitational field strength. Um, that equation is on the equation sheet, right? Yeah. Why would he derive it like that? Actually, it is not quite the same as what is on the equation sheet. It’s not? The equation for buoyant force on the AP Physics 1 equation sheet does not have any f subscripts. Oh! So, without knowing where the equation comes from, you might use the density of the object. Or the volume of the object. And neither of those are right. Right! Right. Class, if the density of an object is less than the density of the fluid displaced by the object, and the object is submerged in the fluid and then released, what will happen to the object? It accelerates upward. Correct. Class, when an object is floating on a fluid, the volume of the fluid displaced by the object is blank the volume of the object? Fill in that blank. less than Correct. Class, when an object is submerged in a fluid, the volume of the fluid displaced by the object is blank the volume of the object? Fill in that blank. equivalent to equal to the same as the same as equal to equivalent to They’re the same. Right. Yeah. Perfect. Next, the four conditions of ideal fluid flow are: The fluid is nonviscous. This means the fluid flows freely with no internal friction. The fluid is incompressible. This means the fluid has a constant density. The flow is steady. The physics term for this is laminar. This means the flow is regular and consistent. And the flow is irrotational. This means the flow has zero net angular velocity. And realize a difference in pressure causes fluids to flow between two locations. Alright, the volumetric flow rate of a fluid is equal to the cross-sectional area of the fluid times the speed of at which the fluid flows. And the continuity equation for ideal fluid flow is the cross-sectional area of plane 1 times the speed through plane 1 equals the cross-sectional area of plane 2 times the speed through plane 2. Another way to say this is that the volumetric flow rate of the fluid is constant. You can see this in this highly idealized animation I made of fluid flowing through a pipe which decreases in diameter. The lines with arrows in them are the streamlines showing the direction of fluid flow and the closer those streamlines are to one another, the faster the fluid particles flow. You can see that the continuity equation for ideal fluid flow demonstrates that, when the cross-sectional area of the pipe decreases, the speed of the fluid flow increases. Oh, and this is ideal flow, so you can see the flow is steady or, in physics terms, laminar And now, Billy, please tell me about Bernoulli’s equation. Certainly! Bernoulli’s equation is a description of mechanical energy remaining constant in ideal fluid flow. Bernoulli’s equation is the pressure at point 1 in a fluid plus one-half times the density of the fluid times the speed of the fluid through point 1 squared plus the density of the fluid times the gravitational field strength times the height of point 1 above an arbitrarily assigned zero line equals all of that again only with subscripts for point 2 instead of point 1. (And what about Bernoulli’s Principle?) Bernoulli’s Principle is the more general concept that relates fluid speed and fluid pressure. In other words, assuming the difference in height is negligible, according to Bernoulli’s Principle, if fluid speed increases, fluid pressure decreases. And we did a whole bunch of fun demonstrations showing Bernoulli’s Principle! Yes, we did. Remember that, to use Bernoulli’s equation, you need to identify the initial and final points, and the horizontal zero line, just like we do when using our mechanical energy equations. And lastly we have Torricelli’s Theorem which can be derived from Bernoulli’s equation. Torricelli’s Theorem gives the speed of an ideal fluid exiting a large, open reservoir through a small hole. Torricelli’s Theorem says that speed equals the square root of two times the gravitational field strength times the depth of the fluid from the top of the fluid in the reservoir to the small hole. We, of course, demonstrated this and derived this. And yes, you definitely need to know how to derive Torricelli’s Theorem. Thank you very much for learning with me today, I enjoy learning with you.