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Calculation templates

Welcome to the Physics library, here we have calculations and content for general physics concepts all the way through to topic areas like fluid mechanics and Astrophysics!

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Thermodynamics and Fluid Dynamics

Acoustics and Optics

Relativity and Quantum Mechanics

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Physics Calculations

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Mach Wave Angle Calculator

Density, Specific Weight and Specific Gravity Calculator

Specific Heats of Solids and Heat Transfer Calculator

Bernoulli Calculator

Hot Air Balloons - Calculating Lifting Force

Froude Number Calculator: Open Channel Flow

Air Density and Specific Weight Calculator

Pressure Calculator

Total and Partial Pressure Calculator

Magnetic Prandtl Number Calculator

Magnetic Reynolds Number Calculator for eddy current braking

Magnetic Reynolds Number Calculator

Reynolds Number Calculator

Reynolds Number Calculator (for motion of a viscous fluid)

Knudsen Number Calculator

Péclet Number Calculator 

Richardson Number Calculator

Bejan Number Calculator

Drag Force and Drag Coefficient Calculator

Diffusion Rate Calculator

View detailed explanations and execute thermodynamics and fluid dynamics calculations.

Physics - Thermodynamics and Fluid Dynamics

Explore material-specific heat data and calculate heat transfer with this calculator.

This page provides insight into determining pressure and some functions to help you calculate it!

Pressure is the normal force per unit area exerted on an imaginary or real plane surface in a fluid, gas or solid.

To calculate pressure, the following equation is used.

Gauge Pressure is the difference between the pressure in a system and the surrounding atmosphere.

If you liked this, check out our other articles and resources!

Bernoulli Equation Calculator: Volume Flow Rate 

Bernoulli Mass Flow Rate Calculator

Free-To-Use Bernoulli Equation Calculator: Calculate Mass Flow Rate for Fluid Mechanics Problems with Ease. Simplify Your Work with CalcTree!

This calculator computes for the lifting force and the mass an air baloon can carry.

The lifting force of a hot air balloon is primarily determined by the buoyant force of the hot air relative to the cold air surrounding it.

When the air inside the balloon is heated, it expands and becomes less dense than the surrounding cooler air. 

This difference in density causes the balloon to float upwards or in other words, it creates a lifting force.

As the lifiting force is equal to the weight or gravity force, the equations can be combined and rearranged to calculate the mass:

Calculate the lifting force of a hot air balloon with this free-to-use tool.

This calculation tool is designed to help you quickly and accurately determine the hydraulic depth of a flowing body of water.

The Froude number, Fr, is a dimensionless value that describes different flow regimes of open channel flow. The Froude number is a ratio of inertial and gravitational forces.

It's used in fluid dynamics to measure the relative importance of gravity and inertia forces in a flow.  The Froude Number can range from 0 to infinity, with 0 representing a flow with no inertia and infinity representing a flow with no gravity.

The Froude number is calculated as the ratio of the inertial force of the flow to the gravitational force of the flow.

The hydraulic depth can be solved by rearranging the formula to solve for flow depth. This is shown below:

Calculate accurate open channel flow on CalcTree. Free-to-Use Froude Number Calculator to enhance your fluid mechanics knowledge. Get started today!

Froude Number Calculator - Open Channel Flow 

degC 

Acceleration due to Gravity m/s^2

Density is a physical property of matter that refers to the mass amount in a given volume. It is usually expressed in units such as grams per cubic centimetre (g/cm^3) or kilograms per cubic meter (kg/m^3). The density of an object can be calculated by dividing its mass by its volume.

Specific weight, or unit weight, is a material's weight per unit volume. It is often used in fluid mechanics and soil mechanics to represent the force exerted by gravity on a unit volume of a material. Specific weight can be calculated by multiplying the material's density by the acceleration due to gravity.

Density is a physical property of matter that refers to the mass amount in a given volume. It is usually expressed in units such as grams per

Air Density and Specific Weight

This page provides insight into determining the total and partial pressure and provides some functions to help you calculate it!

n (of component i)

Partial pressure is used when a mixture of two or more gases in the same volume expresses the pressure caused by each of the individual gases in the mixture.

The total pressure of the gas mixture is the sum of the partial pressure of the component gases.

The total pressure is an expression of the 

From here, we can produce the following expressions for total and partial pressure:

From this, we can say the partial pressure over total pressure is:

Total and Partial Pressure Calculators

Total and Partial Pressure

This tool calculates the Magnetic Prandtl Number, which is a ratio between a fluid's momentum and magnetic diffusivity.

The Magnetic Prandtl Number, calculated from the Reynolds Number, measures the interaction of magnetic fields and fluids. It is a ratio between a fluid's momentum and magnetic diffusivity and is significant for its use in fluid dynamics and magnetohydrodynamics.

The magnetic Prandtl Number can be calculated using the equation below. Since the Reynolds Number and the Magnetic Reynolds Number do not have any units, the Magnetic Prandtl Number is also dimensionless.

This calculator determines Reynolds number, which is the ratio of the inertia forces to the friction forces in flow. Reynolds number is used to determine the transition from laminar flow to turbulent flow in pipes. 

To help solve Reynold's Number, two extra calculators are provided for conversion purposes.

, is a dimensionless number that describes the flow of a fluid. In aerospace engineering, aircraft design can be based on Reynolds number.

Reynold's number can be defined as the ratio of internal forces to the viscous forces within a fluid experiencing relative internal movement due to different fluid velocities. 

For most practical purposes concerning pipes, if the Reynolds number is:

Find out more about laminar vs turbulent flow in the toggle below.

The Reynolds number of fluid is calculated using the following equation;

While the equation is convenient, several assumptions and limitations are observed, such as: 

Also, an adjustment is required to the characteristic length 

 if the fluid flows in a non-circular tube or open channel, wherein the new parameter is used and is called the wetted perimeter. 

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Effortlessly calculate Reynolds number on CalcTree. Free-to-use Reynolds Number Calculator. Optimize fluid flow analysis. Try it now!

This template calculates the magnetic Reynolds number in the context of eddy current braking, which is measure of how well magnetic fields can diffuse (or spread out) within a conducting material, compared to how quickly the magnetic field is advected (or transported) by the conducting material.

The magnetic Reynolds number provides a measure of how well magnetic fields can diffuse (or spread out) within a conducting material, compared to how quickly the magnetic field is advected (or transported) by the conducting material.

The significance of the magnetic Reynolds Number in the context of eddy current braking is that when:

This template calculates the magnetic Reynolds number in the context of eddy current braking.

This template calculates the magnetic Reynolds number which is the ratio of the advection of a magnetic field by fluid motion to magnetic diffusion. The magnetic Reynolds number is used to characterise the relative importance of magnetic effects to fluid flow effects in electrically conducting fluids, such as plasmas and certain liquid metals.

The magnetic Reynolds number is the ratio of the advection of a magnetic field by fluid motion to magnetic diffusion. In simple terms, it provides a measure of how well magnetic fields can diffuse (or spread out) within a conducting fluid, compared to how quickly the magnetic field is advected (or transported) by the fluid flow.

The significance of the magnetic Reynolds Number is that when:

This template calculates the magnetic Reynolds number which is the ratio of the advection of a magnetic field by fluid motion to magnetic diffusion. 

This calculator finds the Knudsen Number, which is the ratio of the molecular mean free path to the physical length scale. It is typically used to determine the regime of fluid flow. 

Knudsen Number is the ratio of the molecular mean free path to the physical length scale, and has a relationship to the Reynolds Number and Mach Number. It is typically used to determine the regime of fluid flow. Knudsen number was named after the Danish physicist Martin Knudsen. 

The rarefaction of flow can be determined from the Knudsen number. The following distinctions of flow can be made using the Knudsen Number:

This calculator finds the Knudsen Number, which is typically used to determine the regime of fluid flow. 

This calculator computes Reynolds number, which is the ratio of the inertia forces to the friction forces in flow. It is used to determine the transition from laminar flow to turbulent flow in pipes.  

A British engineer and physicist, Osborne Reynolds, demonstrated a parameter in 1883 that can determine the transition from laminar to turbulent flow in pipes. The following distinctions of flow can be made using the Reynolds Number.

Reynolds number is crucial in determining fluid behaviour in different scenarios.  In aerospace engineering, aircraft design can be based on Reynolds number. It helps to design more efficient and effective systems.

This calculator computes Reynolds number, which is used to determine the transition from laminar flow to turbulent flow in pipes.  

This template provides two calculation for the Péclet number, one for mass transfer and one for heat transfer. Péclet number provides insight into whether advection or diffusion dominates the transport processes within a fluid flow.

Access the two subpages below for Péclet number describing  mass transfer or heat transfer.

Péclet number (for mass transfer using Reynolds number)

Péclet number (for heat transfer using Reynolds number)

Péclet number provides insight into whether advection or diffusion dominates the transport processes within a fluid flow. 

In engineering applications, the Péclet number is often very large. In such situations, the dependency of the flow upon downstream locations is diminished, and variables in the flow tend to become 'one-way’ properties. Thus, simpler computational models can be adopted when modelling certain situations with high Péclet numbers.

A flow will often have different Péclet numbers for heat and mass. This can lead to the phenomenon of double-diffusive convection.

Péclet number provides insight into whether advection or diffusion dominates the transport processes within a fluid flow.

This calculator computes Richardson Number, which is a dimensionless number used in fluid dynamics to quantify the relative importance of buoyancy forces to inertial forces within a fluid flow. This calculator uses the relationship between Richardson Number, Grashof Number and Reynolds Number which is valid in the context of thermal convection.

Richardson Number is named after Lewis Fry Richardson, a British mathematician and physicist who made significant contributions to meteorology and fluid dynamics.

, which is the transfer of heat from one place to another due to the movement of fluid, the Richardson number represents the importance of natural convection relative to forced convection.

The significance of the Richardson number includes investigating turbidity and density currents in lakes, reservoirs and oceans.

This calculator computes Richardson Number using the relationship with Grashof Number and Reynolds Number which is valid for thermal convection.

Bernoulli Equation Calculator | Calculate Volume Flow Rate

This calculator computes the Bejan Number, which is a dimensionless number used in the Hagen Poiseuille equation to determine the type of flow in a pipe. 

The Bejan number represents the pressure drop along a certain length of pipe when an incompressible fluid flows through it. 

It is a ratio of heat transfer reversibility to total irreversibility due to heat transfer and fluid friction.

Bejan number is used for many heat transfer calculations, including electronic cooling, scale analysis of forced convection, second law analysis of heat exchangers and contact melting and lubrication.

This calculator computes the Bejan Number, which is a dimensionless number used in the Hagen Poiseuille equation to determine the type of flow.

This calculator computes the drag force and drag force coefficient. It also includes a common case study of a sphere in Stokes' flow.

 is the resistance that an object encounters as it moves through a fluid (such as air or water). It acts in the direction opposite to the object's motion which slows it down, and depends on factors like the object's shape, size, speed and the properties of the fluid it's moving through. The drag force increases with the square of the object's velocity and can be significant in aerodynamic or hydrodynamic considerations. 

 is a dimensionless number that quantifies an object's drag in a particular fluid flow. The drag coefficient allows for the comparison of drag efficiency between different objects, irrespective of their size or the specific fluid properties. It plays a crucial role in designing vehicles, structures, or other objects interacting with fluids, providing a standardized measure for their aerodynamic or hydrodynamic performance. The equation for the drag coefficient is given by re-arranging the drag force equation, as provided below:

 refers to a specific regime of fluid flow characterized by low Reynolds numbers 

. Named after the physicist Sir George Gabriel Stokes, this type of flow occurs when the inertial forces within a fluid are negligible compared to the viscous forces. This typically happens in situations with very slow fluid motion, small object sizes, or fluid with high viscosity. In Stokes flow, the equations governing fluid motion simplify significantly and the resulting flow patterns are smooth and predictable. The relationship with drag force becomes particularly interesting in the context of small particles or objects moving through a fluid at low speeds. Stokes' law for flow around a sphere says 

This calculator will help you find drag force and drag force coefficient. Some common study cases for specific shapes and flows have been included.

This calculator computes the density, specific weight and specific gravity of a material or fluid. Density is defined as mass per unit volume of a substance, specific weight measures the weight (force) per unit volume exerted by gravity, and specific gravity compares the density of a substance (i.e., water). These concepts are fundamental for understanding the behavior and characteristics of materials and fluids across various engineering disciplines. 

Particles within a material with a higher density are packed closer together at the atomic level. Density is a physical characteristic that remains constant at a specific temperature and pressure. It can be useful for the identification of substances. 

Unlike density, specific weight is not a fixed property of a material as it depends on the value of the gravitational acceleration. Depending on the material's bulk modulus (i.e. material resistance to compression), pressure may also affect values, however at moderate pressures, it usually has less of an impact than the other variables. Pressure can influence specific weight, but its impact is typically less significant compared to other factors such as temperature. the degree to which pressure affects specific weight depends on the material's bulk modulus. Generally, at moderate pressure, the pressure effect is minor. However, materials with low bulk modulus may experience differently. 

Specific gravity (relative density) is a dimensionless unit defined as the ratio of the density of a substance to the density of water at a specified temperature. It is commonly used the density of water at 

 since water at this point has its highest density of 

Similarly, the specific gravity of gases is defined as the ratio of the density of gases to the density of the air at the specified temperature and pressure. 

This calculator computes the density, specific weight and specific gravity of a material or fluid. 

Mach wave is a pressure wave travelling with the speed of sound caused by a slight change of pressure added to a compressible flow. This calculator computes the Mach wave angle.

In fluid dynamics, a Mach wave is a type of pressure wave that travels at the speed of sound. It is caused by a slight change in pressure within a compressible flow. When multiple Mach waves combine in supersonic flow, they can create a shock wave. If enough Mach waves are present at a location, this shock wave is called a Mach stem or Mach front. By spacing out the production of Mach waves, it is possible to achieve shockless compression or expansion in a supersonic flow. This is known as isentropic compression in supersonic flows. 

A Mach wave moves across the flow at a specific angle called the Mach angle, 

. The Mach angle is the angle between the Mach wavefront and a vector that points opposite the vector of motion. 

👉To calculate the Mach angle, you only need the Mach Number. You can use our 

Minor disturbances are transmitted downstream within a cone for supersonic and hypersonic flows. The green lines in the figure below depict the two-dimensional edge of the cone, moving at velocity 

. Sound waves strike the edge of the cone at a right angle, and the speed of the sound wave is denoted by the letter 

From trigonometry, the sine of the cone angle 

 to a is the Mach number of the flow, that is:

Therefore, we can determine that the cone angle 

Mach wave is a pressure wave travelling with the speed of sound caused by a slight change of pressure added to a compressible flow. 

This calculator computes the diffusion rate of a gas into another gas. Diffusion rate refers to the rate at which particles or molecules spread and move from higher-concentrated areas to lower-concentrated areas. 

Diffusion of a gas is a process by which a net transfer of molecules takes place from a zone in which the gas exerts a high partial pressure to a zone in which it exerts a lower partial pressure. To explain the diffusion of a gas through another gas, we can refer to Graham's law of diffusion, which states that the diffusion rate is inversely proportional to the square root of its molar mass at identical pressure and temperature. Therefore, the smaller the mass of the gas, the faster it will diffuse.

Computes the diffusion rate of a gas into another gas. Diffusion rate is the rate particles move from higher to lower concentrated areas