Question

3. Hot alcohol from a still is cooled in a "worm" liquid-liquid heat exchanger. The alcohol flows through a 2 cm diameter pipe at a rate of 0.5 kg/s and is cooled from 75 to 45 C. Surrounding the pipe is a water bath containing a large quantity of water to keep the outer temperature of the pipe at a constant 20 °C. Use the following properties for alcohol (ethanol): p = 770 kg/m, 5.88 x 104 Ns/m2, k = 0.171, and Cp- 2780 J/(kgK). The properties of water at 20 °C are: p= 99 kg/m2, u=9.85 x 10 Ns/m2, k 0.603, and C, 4182 J/(kgK). Find the length of the pipe (in m (35 points) Alcohol T-750c Pipe Alcohol Te-45°c Weeten balh Water, 20

density of water is998

Answer 1

the formula for pressure difference is

P fX uxp/2 x L/D

Pressure = density x R xT

f can be found from Reynolds number which is given by,

Re = speed x diameter x density / viscosity

= 0.5 x 2 x 10^-2 x 770 /5.88 x 10^-4

= 13095.2

thus f = 0.025

hence,

px R x AT = f x x p/2 x L/D

L Rx AT x 2D/f x u2

= (287.05 J/ Kg K x 30 K x 2 x 2  x 10^-2 )/( 0.025 x 0.25)

= 344.46/6.25 x 10^-3

= 55113.6 m