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 50â—¦. As an alternative
to reduce the temperature, another pipe will run cold water from a lagoon, with
a temperature of 10â—¦ 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 35â—¦ (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.