dimensional
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Chemical processes
![The Prandtl number (Pr) is a dimensionless group that compares the momentum diffusivity to thermal diffusivity for ____.
\[ \text{Pr} = \frac{\nu}{\alpha} = \frac{\mu c_p}{k} \]
Where:
- \( \nu \) = The kinematic viscosity in units of \(\text{meters squared per second (m}^2/\text{s)}\)
- \( \alpha \) = The thermal diffusivity in units of \(\text{meters squared per second (m}^2/\text{s)}\)
- \( \mu \) = The dynamic viscosity
- \( c_p \) = The specific heat
- \( k \) = The thermal conductivity
The units of the kinematic viscosity and thermal diffusivity cancel out, making the Prandtl number dimensionless. This is determined using dimensional analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ba88ecd-654b-4f6b-9783-e93c33ca6a16%2Ff69c60b4-6a57-49c2-a477-f485817063dd%2F3yvu4rp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The Prandtl number (Pr) is a dimensionless group that compares the momentum diffusivity to thermal diffusivity for ____.
\[ \text{Pr} = \frac{\nu}{\alpha} = \frac{\mu c_p}{k} \]
Where:
- \( \nu \) = The kinematic viscosity in units of \(\text{meters squared per second (m}^2/\text{s)}\)
- \( \alpha \) = The thermal diffusivity in units of \(\text{meters squared per second (m}^2/\text{s)}\)
- \( \mu \) = The dynamic viscosity
- \( c_p \) = The specific heat
- \( k \) = The thermal conductivity
The units of the kinematic viscosity and thermal diffusivity cancel out, making the Prandtl number dimensionless. This is determined using dimensional analysis.
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