Question

Fluid Mechanics Chapter 7 Intro

QUESTION 1 If the number of parameters in a problem is m and the number of primary dimensions is 3, then the number of resultant Pl terms is QUESTION 2 If an object travels with a velocity V, a distance, s, in time t. The Pl term formed by using the three variables is QUESTION 3 Friction in the pipe: The shear stress on the pipe-walls (Tw) is a function of flow velocity, V, fluid density (Rh), fluid viscosity (mu), diameter of the pipe (D) and roughness on walls of the pipe (e). The number of Pl terms is QUESTION 4 Sub-questions for Questions #3: Note: The symbol represents raised to the power. i.e. 2^3= 8 PI1 =( Tw)x(V^a1)x (Rh^b1)x (D^c1), where a1= --- , b1 =

Answer 1

Question 18 Il number of paremete es in the ism & the number of primary dimension is 3 , then the resultant pi terms is m-3 . Question 2: Bun Velocity = LIT. Distance = b Time t= T' e gab A Coin mo T = 2'7 a alb coloco mooto= m atib fata Comparing dimensions both side,

ath=o o a=-b - a+c= 0 = a c o Let al = n where foonER ab=-2 for n=1, IT = VET Question 3 - Tw=fC v Rh, mal, D, e) Torell No. of variables m = 6 Primary dimensions n-3 - - No. of r terms = 6-3 = 3 Question 4 Ti = Tu Casa (Rho bloga Tw= mile? T = (m1 7²) (17 ye (mi 3, bl (Le Spn = mi3 mitby, -1 +41-36i+4_-2-01 Comparing dimensions on both e -a-a, = 0 = fa, = -2] VLT