Define the following terms: mass-average velocity, diffusion velocity, stationary medium, and moving medium.

Short Answer

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Define the following terms used in fluid mechanics and mass transport: 1) Mass-average velocity: Mass-average velocity is the weighted average of individual velocities of particles in a fluid mixture, considering their respective masses. It is calculated using the formula: V_m = (Σ m_i v_i)/(Σ m_i), where m_i is the mass of the particle i, v_i is the velocity of particle i, and n is the total number of particles in the mixture. 2) Diffusion velocity: Diffusion velocity is the velocity of a particle or species in a mixture due to concentration gradients, causing particles to move from high concentration areas to low concentration areas. Fick's law is used to determine the diffusion velocity: V_d = -D (dC/dx), where D is the diffusion coefficient, C is the concentration, and x represents the distance in the direction of diffusion. 3) Stationary medium: A stationary medium is a fluid or mixture of particles that are not in motion and have an average velocity of zero. In a stationary medium, properties like pressure, temperature, and concentration are constant, and the concentration gradients drive the movement of particles or species. 4) Moving medium: A moving medium is a fluid or mixture of particles with a non-zero average velocity. In a moving medium, mass transport occurs due to both advection (bulk movement of particles in the flow direction) and diffusion (movement due to concentration gradients). The combined effect of advection and diffusion determines the overall mass transport in a moving medium.

Step by step solution

01

Mass-Average Velocity

Mass-average velocity is the average velocity of a fluid mixture or a mixture of particles with different velocities. It takes into account the individual velocities of each particle and their respective masses. Mathematically, the mass-average velocity (V_m) can be calculated using the following formula: V_m = \frac{\sum_{i=1}^n m_i v_i}{\sum_{i=1}^n m_i} where m_i is the mass of the particle i and v_i is the velocity of particle i, and n is the total number of particles in the mixture. The mass-average velocity represents a weighted average of the individual velocities, where the weights are the masses of the respective particles.
02

Diffusion Velocity

Diffusion velocity is the velocity of a particle or a species in a mixture due to concentration gradients. This movement is driven by the natural tendency of particles to move from areas of higher concentration to areas of lower concentration until a uniform concentration is achieved. The diffusion velocity (V_d) can be determined using Fick's law: V_d = -D \frac{dC}{dx} where D is the diffusion coefficient, C is the concentration of the particle or species, and x represents the distance in the direction of diffusion.
03

Stationary Medium

A stationary medium is a fluid or a mixture of particles that are not in motion, or their average velocity is zero. In a stationary medium, no mass transport occurs, and properties such as pressure, temperature, and concentration are constant throughout the medium or remain the same over time. In the context of mass transport, stationary medium refers to the environment where the concentration gradients are the only driving force for the movement of particles or species.
04

Moving Medium

A moving medium is a fluid or a mixture of particles where the particles are in motion or have a non-zero average velocity. In a moving medium, mass transport occurs due to both advection and diffusion. Advection refers to the bulk movement of particles or species in the same direction as the flow of the medium, while diffusion occurs due to concentration gradients. The combined effect of advection and diffusion determines the overall mass transport in a moving medium.

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