Please show work You are asked to perform a dimensional analysis on a sediment t
ID: 1829154 • Letter: P
Question
Please show work
You are asked to perform a dimensional analysis on a sediment transport problem in the ocean. Let's assume the sediment transport rate, Q. depends on the following variables Q = f{d,H,T,h,w,p,ps,v,g) Where Q = sediment transport rate (M T-1) d = sediment diameter (L) H = wave height (L) T = wave period (T) h = water depth (L) w = sediment fall velocity (L T"1) p = water density (M L-3) ps = sediment density (M L-3) p= water viscosity (ML-1 T-1) g = gravitational acceleration (L T-2) Determine the appropriate Pi groups and the non-dimensional sediment transport rate.Explanation / Answer
A relationship between m variables (physical properties such as velocity, density etc.) can be expressed as a relationship between m-n non-dimensional groups of variables (called p groups), where n is the number of fundamental dimensions (such as mass, length and time) required to express the variables.
So number of non dimension group is 10 -3 = 7
No of repeating variable = 3
Manipulation of the p groups
Once identified manipulation of the p groups is permitted. These manipulations do not change the number of groups involved, but may change their appearance drastically.
Taking the defining equation as: f ( p1 , p2 , p3