Mechanical Calculator

Angular velocity is defined as the rate of change of angular displacement (dθ) with respect to time (dt). Angular velocity (ω) is a measure of the rate of change of angular displacement with respect to time. It describes how fast an object is rotating or how quickly its angular position is changing. Mathematically, it can […]

The Moment of Inertia of a rigid body about a given axis is the sum of the products of each particle’s mass and the square of its distance from the axis of rotation. The Moment of Inertia is measured in kilogram-square meters (kg·m²). The moment of inertia plays a crucial role in rotational dynamics, governing

Conduction heat transfer occurs when thermal energy is transferred from a hotter region to a cooler region within a solid material or between two solid surfaces in direct contact. It’s governed by the temperature gradient across the material and the material’s thermal conductivity. The formula for conduction heat transfer through a material with uniform cross-sectional

Convection heat transfer occurs when a fluid’s motion, caused by density differences due to temperature variations, results in the transfer of thermal energy between a solid surface and the fluid. It’s commonly observed in natural phenomena such as ocean currents, atmospheric circulation, and the cooling of a hot object in air. The formula for convection

Poiseuille’s Law states that the volumetric flow rate (Q) of a Newtonian fluid through a cylindrical pipe is directly proportional to the fourth power of the pipe radius (r) and the pressure gradient (ΔP), and inversely proportional to the viscosity (μ) and the length of the pipe (L). Poiseuille’s Law describes the relationship between flow

The Steady State Mass Transfer Equation states that the mass transfer rate (˙m˙) is proportional to the concentration gradient (dc/dx) and the cross-sectional area (A) perpendicular to the direction of mass transfer. The Steady State Mass Transfer Equation describes the rate of mass transfer through a medium under steady-state conditions.  It’s commonly used in chemical

Rayleigh’s Equation describes the relationship between the pressure fluctuations (p) and the velocity fluctuations (u) associated with acoustic waves in a fluid. It accounts for the compressibility of the fluid and the propagation characteristics of sound waves. Rayleigh’s Equation is a partial differential equation and can vary depending on the specific assumptions and conditions of

The Pressure Gradient Equation describes the change in pressure with respect to distance in a fluid flow field. It’s a fundamental equation in fluid mechanics and is commonly used to analyze the behavior of fluids in pipes, channels, and other conduits. Mathematically, the Pressure Gradient Equation can be expressed as: Where: dP​/dx is the pressure

Laplace’s Law states that the pressure difference (ΔP) across the walls of a spherical shell is directly proportional to the tension (T) in the wall and inversely proportional to the radius (r) of the sphere. Mathematically, it can be expressed as: ​ Where: ΔP is the pressure difference across the wall, T is the surface

Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be expressed as: Where: F is the net force acting on the object, m is the mass of the object,  a is the acceleration