Problem 1.44

Velocity components of a fluid particle are:
u = 3xt, v = 5xy^2, w = 7yz^3, where ^ = raise to the power of

What are the radial velocity (RV) and tangential velocity (TV)?

(3/2 xt^2)i + (5xy^2t)j + (7yz^3t)k
dr/dt = (3xt)i + (5xy^2)j

x = rcosQ, y = rsinQ, e(sub)r = icosQ + jsinQ, where Q = theta

RV = (3rcosQt)(cosQ) + (5r^3cosQsin^2Q)(sinQ)

TV = (3rcosQt)(-sinQ) + (5r^3cosQsin^2Q)(cosQ)

Solution

RV = 3rcos^Qt + 5r^3cosQsin^3Q
TV = -3rcosQsinQt + 5r^3cos^2Qsin^2Q

Problem posted 6/23/05 -- LAL