Question

Question 1 If Glycerine is pumped through a horizontal pipe, with 50 mm diameter and 65 m length, at a rate Q-4.5x10 m/s. If the flow is steady and fully developed, then do the following: (1) Calculate Reynold number, Re, and show the flow is laminar [3 marks (ii) calculate the friction factor, f, [2 marks] (iii) determine the total head loss, Ah, [3 marks (iv) determine the wall shear stress, tw. [4 marks) Take the density and dynamic viscosity of Glycerine as p=1260 kg/m' and u -0.9 respectively.

Answer 1

In the given problem Reynolds number is calculated using the formula Re = $\rho$ VD / $\mu$

Then for laminar flow friction factor(f) = 64/Re

Total head loss($\Delta$h) = fLV2 / 2gd

For wall shear stress the formula $\tau$ w = ($\Delta$p/$\Delta$x)*(R/2)

Given, diameter of pipe (d) - somm= 0.05m length of pipe (1)= 65m flow rate (0)= 4.5x10 muß sec density (e) = 1260 kg/m² (i) Reynolds Numbers per evD M = 0.9 we do that, Q-Axv. 4.5x103 (0.05) x v velocity = = 2.29 m/sec Now, kerrolds Nurser- 1260 +2.29 x 0.05 09 Re - 160.31 & The flow in laminar since Re<2000. (11) Friction factor (+): for laminar flow, to see 64 1603 f = 0.399

(1) Total head lois (oh) sh= ELV² agd 0.399 x 65* 2.29) 2x9.81* 0.05 on = 138-82m] (iv) Wall shear stress (tw): we trou, w e e do & -(e) auta OP - 4.5x10 .09. Tx (0.025) 4 dx Now, (P) & - 45*10**0- 20.035) Tx (0.025) Tw= 41.253 font] 41.253
​​​​​​​