--- title: "AP Physics 1 Fluids Dynamics Speed Review" description: "This engaging, no-fluff review covers pressure, buoyancy, Bernoulli’s principle, and key equations—so you can master the topic fast." featured_image: "https://nerd-notes.com/wp-content/uploads/2025/03/seth-doyle-b5ul8TBY0S8-unsplash-1-1.jpg" url: "https://nerd-notes.com/ap-physics-1-fluids-dynamics-review-key-equations-concepts-made-easy/" date_modified: "2026-11-02T13:50:13+00:00" --- # AP Physics 1 Fluids Dynamics Speed Review ## Attribution Guidelines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarizing, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/ap-physics-1-fluids-dynamics-review-key-equations-concepts-made-easy/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/ap-physics-1-fluids-dynamics-review-key-equations-concepts-made-easy/ This post will cover everything you need to know for fluids in 15 minutes or less with targeted practice. ### The Ultimate Fluids Speed Review This guide will get you up to speed with everything you need to know about **fluids, pressure, buoyancy, and flow**. After you’re done take this [10 questions fluids quiz](https://nerd-notes.com/quiz/?id=32) for mastery. Check out the [Youtube Fluids Speed Review](https://www.youtube.com/watch?v=uubzy_lNCV8) if you prefer watching me derive equations fluid principles from scratch. Let’s get into it. Understanding Bernoulli’s Principle Official course · step-by-step video walkthrough [Watch · 21 min](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=ap-physics-1-fluids-dynamics-review-key-equations-concepts-made-easy&utm_content=video-mid#course=94339&module=98826&lesson=110494) ### First Things First: What Even is a Fluid? Fluids are anything that flows. Think liquids, gases, and whatever weird in-between states physics hasn’t classified yet. Unlike solids, fluids don’t hold their shape; they take the form of whatever container they’re in. The key quantity to track? **Density**, which is just mass packed into a given volume: \[ \rho = \frac{m}{V} \] [Remove Ads](https://nerd-notes.com/pricing/?for=students) Think about it: oil floats on water because it’s less dense. Helium rises in air for the same reason. Simple. Try applying it: [Open in UBQ](https://nerd-notes.com/ubq/87425/) Question 15 Diamond has a density of 3500 kg/m³. During a physics lab, a diamond drops out of Virginia's necklace and falls into her graduated cylinder filled… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=ap-physics-1-fluids-dynamics-review-key-equations-concepts-made-easy&utm_content=top) ### Pressure: The Invisible Force You Never Notice Pressure is how much force a fluid applies over an area. Mathematically, that’s: \[ P = \frac{F_{\perp}}{A} \] More force? More pressure. Smaller area? Even more pressure. #### A Note on Pascal’s Law Normally, this is where we’d talk about Pascal’s Law which explains how a change in pressure is transmitted equally throughout an enclosed fluid. It explains how hydraulic systems work, like the braking system in your car. A small force applied at one end can create a much larger force at the other, making it possible to stop a car with just the pressure from your foot. The equation for Pascal’s Law is: \[ F_1 = \frac{A_1}{A_2} F_2 \] It’s important to note that Pascal’s Law is **not** covered on the AP Physics 1 exam (but it’s simple and easy to understand). Try it out: [Open in UBQ](https://nerd-notes.com/ubq/86798/) Question 16 The radius of the left piston is 0.12 m and the radius of the right piston is 0.65 m. If f were raised by 14 N, how much would F need to be increased… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) #### How Fluid Pressure Changes with Depth Pressure increases with depth because more water weight presses down from above. For a fluid column the pressure is still \(\dfrac{F}{A}\). But measuring force (of fluid weight) is impractical. So we use density as a helper equation \(\rho = \dfrac{m}{V}\) and combine it with the previous equation to get: \[ P = \dfrac{F}{A} = \dfrac{mg}{A} = \dfrac{\rho Vg}{A} = \boxed{\rho gh}\] This formula is what we call **gauge pressure**, also known as fluid pressure. [Open in UBQ](https://nerd-notes.com/ubq/107013/) Question 17 The gauge pressure at a certain depth in a fluid is P_gauge. If you dive to a depth that is twice as deep in the same fluid, what will the new gauge… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) #### Absolute Pressure A cup of water experiences **gauge pressure** from the water itself and atmospheric pressure from the air pushing down on its surface. The sum of these two is known as total, or absolute, pressure. The equation for absolute pressure is: \[ P = P_0 + \rho gh \] Where \(P_0\) is atmospheric pressure at the surface. Pressure under water nerd-notes.com *Both lines rise by \(\rho g \approx 9.8\,\text{kPa}\) per meter of depth. Absolute pressure starts at \(P_0 \approx 101\,\text{kPa}\) at the surface; gauge pressure starts at zero.* Try applying it here: [Open in UBQ](https://nerd-notes.com/ubq/87424/) Question 18 Wanda watches the fish in her fish tank and notices that the angelfish like to feed at the water’s surface, while the catfish feed 0.300 m below at… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Buoyancy: Why Some Things Float and Others Sink Ever tried to push a beach ball underwater? The harder you push, the stronger the water pushes back. That’s **buoyancy** in action. Archimedes figured out that the buoyant force equals the weight of the **displaced fluid** (\(\text{DF}\)): \[ F_b = m_{DF}g = \rho_{DF} V_{DF} g \] So the further you push down the beach ball, the more water it will displace, creating a larger buoyant force. Note: buoyant force does NOT come from the weight of the OBJECT itself. [Open in UBQ](https://nerd-notes.com/ubq/81521/) Question 19 A small rock sits at the bottom of a cup filled with water. The upward force exerted by the water on the rock is F₀. The water is then poured out and… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) If \(F_b\) is greater than the object’s weight, it rises until \(F_b\) equals its weight, then floats. If \(F_b\) is less than its weight even when it is fully underwater, down it goes. \(F_b\) \(mg\) \(F_b = mg\) \(F_b\) \(mg\) \(F_b < mg\) *A floating block sinks until it displaces its own weight of fluid, so \(F_b = mg\). A denser block can’t displace enough: \(F_b < mg\) and it sinks.* This also explains why ships, despite being made of heavy metal, don’t sink: they displace enough water to generate a buoyant force equal to their own weight. [Open in UBQ](https://nerd-notes.com/ubq/79408/) Question 20 Two objects labeled K and L have equal mass but densities 0.95Dₒ and Dₒ, respectively. Each of these objects floats after being thrown into a deep… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) #### Problem Solving With Buoyant Forces Follow the forces problem framework: 1. Draw an FBD. Keep in mind fluids, including air, have weight! 2. Sum up forces and use newton’s law \(F = ma\) 3. Derive! If you need, plug in the formula for buoyancy and solve for the unknown. Try it out this question: [Open in UBQ](https://nerd-notes.com/ubq/87421/) Question 21 A spherical balloon of mass 226 kg is filled with helium gas until its volume is 325 m³. Assume the density of air is 1.29 kg/m³ and the density of… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=ap-physics-1-fluids-dynamics-review-key-equations-concepts-made-easy&utm_content=mid) ### Fluid Flow: Conservation Of *Mass* Fluids follow a strict rule: what goes in must come out. That’s where the **continuity equation** comes in: \[ A_1 v_1 = A_2 v_2 \] Here’s what it really means: the volume of fluid flowing per second stays the same, no matter how the pipe’s shape changes. This is called the **flow rate** (\( Q \)), defined as: \[ Q = A v \] Where: - \(Q\) = flow rate \(\frac{m^3}{s}\) - \(A\) = cross-sectional area \(m^2\) - \(v\) = velocity of the fluid \(\frac{m}{s}\) If a pipe gets narrower, the velocity increases to maintain the same flow rate. If it widens, the velocity decreases. That’s why river rapids form when a wide river suddenly narrows—water speeds up to keep the same volume moving through. **The flow rate always stays constant for an incompressible fluid.** If area changes, velocity adjusts to compensate. [Remove Ads](https://nerd-notes.com/pricing/?for=students) Try it out: [Open in UBQ](https://nerd-notes.com/ubq/81524/) Question 22 A fluid flows through the two sections of cylindrical pipe shown in the figure. The narrow section of the pipe has radius R and the wide section has… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) ### Bernoulli’s Equation: Conservation of Energy (Revisited) Bernoulli’s principle is just conservation of energy applied to fluids. It states that a fluid’s total energy (pressure, gravitational potential, and kinetic) stays constant: \[ P_1 + \rho g y_1 + \frac{1}{2} \rho v_1^2 = P_2 + \rho g y_2 + \frac{1}{2} \rho v_2^2 \] In short, a gain in one form of energy must come from a decrease in another. For example, consider what happens when a pipe narrows: the fluid speeds up (according to continuity). But that increase in kinetic energy has to come from somewhere — and it comes from pressure. \(v_1\) \(v_2\) \(A_1 \text{ big}\) \(A_2 \text{ small}\) \(\text{slow, high } P_1\) \(\text{fast, low } P_2\) \(A_1 v_1 = A_2 v_2\) *Where the pipe narrows, the fluid speeds up to keep the flow rate (\(A_1v_1 = A_2v_2\)), and the faster fluid has lower pressure (Bernoulli).* This explains: - How airplanes generate lift (faster air over top of wing = lower pressure at top compared to bottom) - Why a shower curtain gets sucked inward when you turn on the water - How a perfume atomizer sprays liquid Try it out: [Open in UBQ](https://nerd-notes.com/ubq/79300/) Question 23 Water flowing in a horizontal pipe speeds up as it goes from a section with a large diameter to a section with a small diameter. Which of the… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/107163/) Question 24 Two points, A and B, are in a pipe carrying a flowing ideal fluid. Point B is 2.0 m higher than point A, and the fluid speed at B is twice the speed… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) #### Torricelli’s Theorem: Fluid Speed Without the Drama When a fluid drains out of a hole, it acts like it’s in free fall. Torricelli’s equation gives its speed: \[ v = \sqrt{2g\Delta y} \] The greater the height difference, the faster the fluid moves. That’s why water from a tall tower shoots out faster than from a short one. [Open in UBQ](https://nerd-notes.com/ubq/107166/) Question 25 Water exits a small hole at the bottom of a large, open cylindrical tank. If the height of the water level above the hole is H, the exit speed is v… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) --- ### Final Takeaways (a.k.a. Your Cheat Sheet) - Fluid pressure increases with depth: \( P = \rho gh \) - Buoyant force = weight of displaced fluid: \( F_b = \rho V g \) - Fluid flow speeds up in narrow spaces: \( A_1 v_1 = A_2 v_2 \) - Fast-moving fluids have low pressure: Bernoulli’s equation - Fluid draining from a hole follows \( v = \sqrt{2g\Delta y} \) Master these, and you’ll crush any fluids question the AP throws at you. If you’re looking for [free fluid practice questions](https://nerd-notes.com/ubq/) in AP style, check out UBQ, our collection of over 1000+ Physics questions, with explanations, AI powered assistance, and automatic FRQ grading. Over 200,000 students use it daily to accelerate this success! Try it [here](https://nerd-notes.com/ubq/). If you need questions already organized into quizzes try Quiz Labs. ### More Practice Questions for Mastery [Open in UBQ](https://nerd-notes.com/ubq/79313/) Question 26 A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/80386/) Question 27 Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter. The pipe… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/81535/) Question 28 A fountain with an opening of radius 0.015 m shoots a stream of water vertically from ground level at 6.0 m/s. The density of water is 1000 kg/m³. 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