Question

7. (10 points) The pressure drop, AP, for flow through an orifice plate is a function of the orifice diameter d, the pipe diameter D, fluid density, p, fluid viscosity, H, and average velocity, v. Use the method of repeating variables to determine the appropriate dimensionless relationship.

Answer 1

solution, Step Li Using method of repeating variables. determine number of variables & ho. of fundamental dimensions here, ДР d D. S. M. v 2 where AP = Pressure drop orifice diameter pipe diameter fluid density fludd viscosity Average relocity no. of variables, h = 6 (AP, d, D, S, M, V) how write dimensions of each variable [AP] = [ MLT-2] [d] = [L] [0] [L [p] = CM2^3

Date: Page: (u] = (MLT-1 [Q ] [LT" here M. L T mass Length time m = 3 no. of fundamental dimensions , (M, L, I, Step 2: determine number of dimensionless t-terms: no. of - terms no. of independent dimensionless groups n-m 6-3 3 (a, , , ) Also, no. of repeating variables no. of fundamental variables. 3 step 3: Choose repeating variables: such that So, 3 Repeating variables are chosen such that a vardable represents geometric property we are choosing pipe diameter D را

Date : Page : we i variable represents flow property are choosing velocity e variable represents fluid property we are choosing density s. Step 4: Assign X-terms: lü ) het 4 지 BAP Repeating variables an be D. vs. d 43 bz 13 = De vil. M Step si Dimensional analysis to determine 2, R & Rz. Do vos". Al bi a+b, -3G-1 I Moloto] [L]. [LT] [ ML-37". [ MLT-2 = [ Mo Lo To [M] 9+1 [Luth on comparing exponents of ML, AT [7]aby?

Date : Page: 2) o= Gt1 0 = -b, 2 bi atb, -39-1 a - 2 - 3(-1)-) 3 0 = a to a = 0 지 Dow? gal DP 2 파 др. sve aus bz ar CL be ged (MLoTo [LT] [ ML-37. [l = (mag. [ Las the -34 +1] [t be] 3 [M° Loto On comparing 0= a 기 aby=0 at b₂ - 3G + 1 xo= a to 310) ti - vos d ha d 기

Date : Page : 5, .63 I My = D. vis u CM° Loto] = [ 2793 [ LT-1] 3 [ ML-37% [ Mily" 93 + by (M° L T J = [M 1 [u -303 -1 ] [T 3-'] On comp. qt 거 - bz-l bz - Azt bz-3G-1 [ Mesti 21 20 = 92 - 1-3(-)-1 at 1 a az = -1 D. V. S. D.V.S Step 6: Relate to the x = f( 7 A3) Pous) ΔΡ Suz fla 구 Reynold's no. ( Re = PUD - ΔΡ. sur or Re M