While researching fluid dynamics, you come across a reference to the dimensionless number called the capillary number, given by the equation below. Са3 Y where: fluid viscosity velocity g/(m s) ] ft s What are the dimensions of gamma, y? Click the icon to view the table of fundamental dimensions and base units The dimensions of variable y are (Type a product of fundamental dimensions each indicated with an exponent as needed. Use symbols provided in the table of fundamental dimensions.) Unit Dimension Symbol Symbol Length L meter m Mass М kilogram kg Time T second Temperature kelvin К Amount of substance mole mol Light intensity J candela cd Electric current A ampere

While researching fluid dynamics, you come across a reference to the dimensionless number called the capillary number, given by the equation below. Са3 Y where: fluid viscosity velocity g/(m s) ] ft s What are the dimensions of gamma, y? Click the icon to view the table of fundamental dimensions and base units The dimensions of variable y are (Type a product of fundamental dimensions each indicated with an exponent as needed. Use symbols provided in the table of fundamental dimensions.) Unit Dimension Symbol Symbol Length L meter m Mass М kilogram kg Time T second Temperature kelvin К Amount of substance mole mol Light intensity J candela cd Electric current A ampere

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 1.6CYU: Check Your Understanding Is the equation v=atdimensionally consistent? One further point thin needs...

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Check Your Understanding Is the equation v=atdimensionally consistent? One further point thin needs to be mentioned is the effect of the operations of calculus on dimensions. We have seen that dimensions obey the rules of algebra, just like units, but what happens when we take the derivative of one physical quantity with respect to another or integrate a physical quantity over another? The derivative of a function is just the slope of the line tangent to its graph and slopes are ratios, so for physical quantities vand t , we hive that the dimension of the derivative of vwith respect to us just the ratio of the dimension of v over that of t : [dvdt]=[vt] . Similarly, since integrals are just sums of products, the dimension of the integral of vwith respect to t is simply the dimension of vtimes the dimension of t : [vdt]=[v][t] . By the same reasoning, analogous rules hold for the units of physical quantities derived from other quantities by integration or differentiation.
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