Engineers and investors are planning to build a luxury hotel at Yellowstone. They

have the rights to exploit hot springs located in the mountains. The water coming

from the hot spring is very hot, reaching a temperature of 50?. As an alternative

to reduce the temperature, another pipe will run cold water from a lagoon, with

a temperature of 10? and mix it with the hot water. The engineers realized that

this is a very complex problem for Hazen-Williams model because such a model

would consider water at same temperature. The engineers, therefore, will employ

the Darcy-Weisbach formulation. They remark that kinematic viscosity will change with temperature. They present the kinematic viscosity as a function of temperature (below). The pipe is commercial steel with ks=0.046.

(a) Determine the flow rates extracted from the hot and cold sources so the total flow

rate is 20 [l/s] and the temperature after mixture is 35? (i.e. define the correct

proportion of Q from each pipe so you get the correct mixed temperature).

Assume an instantaneous and adiabatic mixing (i.e. the temperature can be

obtained by simply calculating the ratios of flow rate from each pipe).

(b) Determine the diameter of the hot and cold pipes coming from the cold and

hot water sources. Hint: You need to use the Moody Abacus for each of the

two pipes. You need to iterate for the diameters. In the first iteration you

need to guess the diameters. Then you get the values of f. Then use those f in

the Bernoulli equation with the diameter as unknown. If the values of D are

different from the first guess, perform another iteration.