Question 10.1: Compare the lost head for water and a 30 percent ethylene gl......

Equation 10-6 will be used. From Table C-1 the inside diameter of 3 in. nominal diameter Schedule 40 pipe is 3.068 in. and the inside cross-sectional area for flow is 0.0513 ft². The Reynolds number is given by Eq. 10-10, and the average velocity in the pipe is

l_{f}  =  f  \frac{L}{D}  \frac{\bar{V}^{2}}{2 g}                    (10-6)

Re  =  \frac{ρ  \bar{V}  D}{μ}  =  \frac{\bar{V}  D}{\text{v}}                (10-10)

\bar{V}  =  \frac{\dot{Q}}{A}  =  \frac{110  gal/min}{(7.48  gal/ft³) (0.0513  ft²)}  =  287  ft/min  =  4.78  ft/sec

The absolute viscosity of pure water at 50 F is 1.4 centipoise, or 9.4 × 10^{-4} lbm/ (ft-sec), from Fig. 10-2b. Then

Re  =  \frac{62.4  (4.78)  (3.068/12)}{9.4 ×  10^{-4}}  =  8.1  ×  10^{-4}

From Fig. 10-1 the absolute roughness e is 0.00015 for commercial steel pipe. The relative roughness is then

e/D = 12(0.00015/3.068) = 0.00058

The flow is in the transition zone, and the friction factor f is 0.021 from Fig. 10-1. The lost head for pure water is then computed using Eq. 10-6

l_{fw}  =  0.021  ×  \frac{200}{3.068/12}  ×  \frac{(4.78)²}{2(32.2)}  =  5.83  ft  of  water

The absolute viscosity of the 30 percent ethylene glycol solution is 3.1 centipoise from Fig. 10-2b, and its specific gravity is 1.042 from Fig. 10-2a. The Reynolds number for this case is

Re  =  \frac{1.042 (62.4)  (4.78)  (3.068/12)}{3.1/1490}  =  3.8  ×  10^{4}

and the friction factor is 0.024 from Fig. 10-1. Then

l_{fe}  =  0.024  ×  \frac{200}{3.068/12}  ×  \frac{(4.78)²}{2(32.2)}  =  6.66  ft  of  E.G.S.

=  6.94  ft  of  water

The increase in lost head with the brine solution is

Percent increase  =  \frac{100 (6.94  –  5.83)}{5.83}  =  19  percent