--- title: "Mach Number in Thermodynamics II" description: "Mach Number is the ratio of flow speed to the speed of sound, and it tells you when compressibility, shocks, and stagnation changes matter in Thermodynamics II." canonical: "https://fiveable.me/thermodynamics-ii/key-terms/mach-number" type: "key-term" subject: "Thermodynamics II" unit: "Unit 11" --- # Mach Number in Thermodynamics II ## Definition Mach number is the ratio of an object's speed to the speed of sound in the surrounding fluid. In Thermodynamics II, it tells you whether a flow is subsonic, sonic, supersonic, or hypersonic and whether compressibility effects matter. ## What It Is Mach number is a dimensionless ratio that compares a flow velocity to the local speed of sound, written as M = V/a. In Thermodynamics II, it is one of the first numbers you check when analyzing compressible flow, because it tells you how strongly the gas will respond to acceleration, deceleration, and pressure changes. The big idea is that sound speed is not just a property of the object moving through the gas. It is a property of the gas itself, so Mach number depends on the medium and its state. In air, the speed of sound changes with temperature, which means the same aircraft speed can give different Mach numbers at different altitudes. That matters because low Mach and high Mach flows behave differently. At low Mach numbers, pressure changes travel through the fluid fast enough that density changes are often small. As Mach number rises toward 1, compressibility effects become hard to ignore, and the flow can no longer be treated like an almost-incompressible fluid. Around Mach 1, the flow reaches the sonic condition. That is the point where the fluid speed matches the local speed of sound, and it is where many compressible-flow relations switch behavior. Nozzles, diffusers, and ducts can show sharp changes here, and a small change in back pressure can flip a flow from smooth to one with a shock wave. Above Mach 1, the flow is supersonic, which means pressure disturbances cannot move upstream through the gas the way they do in subsonic flow. That is why shocks form, and why normal shock and oblique shock relations show up in Thermodynamics II. In very high-speed flow, often above about Mach 3, the term hypersonic is used, and the effects become even more severe. A common mistake is to treat Mach number as a fixed property of a vehicle. It is really a local flow ratio, so two points in the same duct or around the same body can have different Mach numbers. In problems, you usually compute it from the local velocity and the local speed of sound, then use that value to choose the right compressible-flow equations. ## Why It Matters Mach number is the switch that tells you which compressible-flow model to use in Thermodynamics II. If you misread it, you can choose the wrong equations for stagnation properties, pressure ratios, or shock calculations and end up with answers that are physically impossible. It also connects directly to real engineering devices. In a nozzle problem, Mach number tells you whether the flow is accelerating smoothly or choking at the throat. In a diffuser or inlet, it tells you whether the gas can slow down without a shock or whether a shock must appear to satisfy the downstream pressure. This number shows up again when you interpret how temperature, pressure, and density change across a flow field. For isentropic flow, Mach number lets you relate local conditions to stagnation conditions. For shock waves, it tells you how severe the jump will be and whether the upstream flow is strong enough to support a normal shock or oblique shock. If you are working through problem sets, Mach number is usually the first checkpoint before any deeper calculation. It tells you whether the flow is subsonic, sonic, or supersonic, which determines the formula set and the physical story you should describe in your solution. ## Connections ### Speed of Sound Mach number is built from the speed of sound, so you cannot find M without knowing the local acoustic speed. In Thermodynamics II, that usually means checking the gas temperature first, since warmer gas generally has a higher sound speed. This is why Mach number can change with altitude even if the object's actual velocity stays the same. ### Isentropic Flow Mach number is the main variable in isentropic compressible-flow relations. Once you know M, you can connect it to pressure, temperature, and density ratios for smooth, shock-free flow. That is why nozzle and diffuser problems often start with Mach number before moving to stagnation properties. ### Shock Wave When the flow is supersonic, Mach number helps predict whether a shock wave will form and how strong it will be. A normal shock or oblique shock causes sudden jumps in pressure, temperature, density, and entropy, and the upstream Mach number sets the size of those jumps. ### [Critical Mach Number](/thermodynamics-ii/key-terms/critical-mach-number) Critical Mach number is a more specific threshold than Mach 1, and it usually comes up when flow over a body first reaches sonic speed at some point on the surface. It is easy to confuse with the overall free-stream Mach number, but the critical value is about local acceleration around the body. ## On the AP Exam A quiz or problem set will usually give you a velocity, gas temperature, or both, and ask you to find Mach number before choosing the right flow model. If the result is below 1, you usually stay in the subsonic or isentropic range. If it is above 1, you should be ready to use shock relations, pressure ratios, or stagnation-property equations that apply to compressible flow. You may also need to interpret a diagram or device description and decide whether the flow is choked, supersonic, or likely to contain a shock. The main move is not just calculating M, but using it to explain what the gas can and cannot do. A good written answer names the regime and then connects that regime to pressure, temperature, and velocity behavior. ## Mach Number vs Critical Mach Number Mach number is the ratio of flow speed to local speed of sound anywhere in the flow. Critical Mach number is the free-stream speed at which some point on a body first reaches Mach 1. One is a local flow ratio, the other is a threshold tied to surface acceleration around an airfoil or body. ## Key Takeaways - Mach number is the ratio M = V/a, so it compares flow speed to the local speed of sound, not to some universal fixed speed. - In Thermodynamics II, Mach number tells you whether compressibility effects are small, noticeable, or dominant in a flow problem. - When Mach number approaches 1, pressure, density, and temperature can change sharply, and shock waves may appear. - Supersonic flow does not let pressure signals travel upstream the way subsonic flow does, which is why the equations and flow behavior change. - Always check the local speed of sound first, because temperature changes can change Mach number even if the actual velocity stays the same. ## FAQs ### What is Mach Number in Thermodynamics II? Mach number is the ratio of a fluid's speed to the speed of sound in that fluid. In Thermodynamics II, it tells you whether the flow is subsonic, sonic, supersonic, or hypersonic, which decides what equations you use for compressible flow. ### How do you calculate Mach Number? Use M = V/a, where V is the local flow speed and a is the local speed of sound. If temperature changes, a changes too, so you need the state of the gas at the point you are analyzing, not just the object's speed. ### Is Mach Number the same as speed? No. Speed is measured in units like m/s or ft/s, while Mach number is dimensionless. Two flows can have the same speed but different Mach numbers if the local speed of sound is different because the gas temperature or composition is different. ### Why does Mach Number matter for shocks and nozzles? Mach number tells you whether the flow can stay smooth or whether it may form a shock. In nozzles, it helps identify choking and supersonic acceleration. In shocks, the upstream Mach number controls how large the pressure and temperature jumps will be. ## Related Study Guides - [11.2 Normal Shock Waves and Oblique Shocks](/thermodynamics-ii/unit-11/normal-shock-waves-oblique-shocks/study-guide/AljYAB9qYOdkeHEY) - [11.1 Stagnation Properties and Isentropic Flow](/thermodynamics-ii/unit-11/stagnation-properties-isentropic-flow/study-guide/YkPOzRSJps7BAIbf) ## About This Document Canonical Fiveable pages are available as Markdown at the same path plus `.md`. - [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns - [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing - [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`) - [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`) ## Structured Data ```json {"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/thermodynamics-ii/key-terms/mach-number#resource","name":"Mach Number in Thermodynamics II","url":"https://fiveable.me/thermodynamics-ii/key-terms/mach-number","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/thermodynamics-ii/key-terms/mach-number#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-07-03T02:24:17.747Z","isPartOf":{"@type":"Collection","name":"Thermodynamics II Key Terms","url":"https://fiveable.me/thermodynamics-ii/key-terms"},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/thermodynamics-ii/key-terms/mach-number#term","name":"Mach Number","description":"Mach number is the ratio of an object's speed to the speed of sound in the surrounding fluid. 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