Mass flow rate for six pumps. Given in gallons per hour,
converted to kg per second.
Figure 3 Pump system with input and output water paths.
Model # 2
Determine the exit water temperature to verify that
it is not lower than 23 C. Chose a pump that will give
an exit water temperature of approxatmatly 23.5 C.
Given:
Input energy, as determined from Model # 1. Intial
temperature, heat capicity of water, mass flow rate
for six different pumps. (210gph, 250gph, 450gph, 700gph,
750gph, 1200gph)
Assumptions:
No heat loss in pipes, no mechanical energy losses
in pipes.
The energy required for the system to be in steady state
is 3.7 watts This is for an initial temperature of
27 C. These values will now be substituted into the
next set of calculations to determine the mass flow
rate and ultimatly the pump.
Energy ballance equation
for the system
Resistance Totals: The
Rleft
corrospondes to the shell and insulation closest to
the magnet bore and the Rright
corrospondes the shells and insulation closest to the
sample.
The calculations presented here were used to detemine
system parameters for the design of the yeast cultavator.
The system models were developed with the help of Dr.
Haik, see Appendix M Meeting notes. Revisions may be
done on these calculaions as the system developes.
Calculations by : James Sizemore
Approved and Checked by: Andrew Parry
Pump:
400 gph
Exit Water Temperature: 24.8 C
In the first set of the calculations a 400 pgh pump
was selected. However, these calculations suggest
a 250 to 350 gph pump. The pump chosen here will be
the same as before, 400 gph pump, this is for these
reasons:
1) Head loss will be introduced into the system by changing
the relative height betwen the pump and the water jacket.
When this system is used in the lab the pump may be
required to set several feet below the water jacket.
This will be used to lower the mass flow rate if necessary.
2) The over compensation of the pump size will allow
for other losses that may occure in the system.
The mass flow rate determined from graph below was between
0.25082 kg/s and
0.37082 kg/s.
This corresponds to 250 gph and 35
0 gph pumps.
Some head loss will be expected, for this reason the
pump with the greater mass flow rate will be selected.
The exit water temperature used for the pump selection
was between
23.46 C and 24.61 C.
The mass flow rate is varried to incorporate all the
listed pumps above. This will allow the outlet temperture
of the water to be graphed as a function of the mass
flow rate.Mass flow is in SI, kg/s.
Given values: Heat capacity for water and intial inlet
temperture for the supply water. The units are SI
L is the height of the
system, X1-3
are the wall thicknesses, w's are the thicknesses for
the two insulation layers and the water jacket. The
r's are the values for the the raduii. The values are
given in cm and are then conveted to meters for the
calculations. See Figure 2 below.
Thermal conduction factors for alluminum and the insulation
Given temperatures for the sample, outside temperature,
and the water sample.
Model # 1
Determine the amount of energy, in watts, needed to
maintain the sample at 23 C. Determine the thickness
of the insulation that will give optimal thermal resistance
for the available area. The temperature of the water
will be given an initial value close to that of the
sample. This temperature will be checked for accuracy
in Model # 2.
Given:
The sample must remain at 23 C. The surrounding
temperature is 8 C. The wall thickness are different
for each cylinder. Initial trial value for the water
temperature is 27 C. The height of the system (outer
shell) is 25 cm.
Assumptions:
Steady state, one dimensional heat flow, no convection
on outside wall, the energy into the system is equal
to the energy going to the sample and the outside wall,
Qin
= Qoutside
+ Qsample
.
System Model:
Revision # 1:
The calculations for the design needed to be changed
due to material constraints. The intial calculations
called for cylinders sizes that are not commonly manufactured.
To get around this problem, cylinders with common sizes
were chosen. The outter most cylinder in the first
design and set of calculations was ellimanated because
the size is not manufactured. This change is the main
reason for this revision of the first set of calculations.
The system model was analyzed using energy balance.
It was broken into two separate models. The first model
was used to determine the energy supplied to the system
Qin
(watts)
. The second model was used to determine the temperature
of the the water after it leaves the water bath and
the its' mass flow rate. The output temperature of
the water should not be less than the temperature of
the sample, 23 C.
Resistance equations for the cylindrical shells
Fi
gure 2 Cut away of the Resistance network for one side
w ins1 x2 w water
x3 w ins2 x4
Thermal resistance approach
Q = Ti
- Tf /
Rtotal. The flow of energy, for this model, goes to
the left and to the right. It was for this reason the
model was analyzed in two parts, the left and the right.
Each side having different thermal resistance due to
their different geomertries.
