CoCalc -- 2015-09-30-R-value-calculation.ipynb

Jupyter notebook 2015-09-30-R-value-calculation.ipynb

Project: ENSP 337

Path: 2015-09-30-R-value-calculation.ipynb

Views: ⁶²

Kernel: Python 2 (SageMath)

The code below tells the computer that each of the variables (watt, ft, ...) represent a unit.

In [2]:

from pint import UnitRegistry
u = UnitRegistry()

In [3]:

length = 30 * u.meter
width = 30 * u.meter
length * width

Out[3]:

In [4]:

(length * width).to(u.feet**2)

Out[4]:

In [0]:

In [0]:

In [0]:

In [1]:

K = ureg.degK
m = ureg.m
watt = ureg.watt
ft = ureg.ft
hour = ureg.hour
BTU = ureg.BTU
F = ureg.degR

This is the representation in mathematics

k_{wood} = 0.15 \frac{watt}{K \cdot m}

R_{wood} = \frac{t_{wood}}{k_{wood}}

R_{total} = R_{wood} + R_{foam} + R_{wood}

Below is an implementation of the calculation in Python code with units.

We define the conductivities of wood and foam using values from a table in Wikipedia. We also define the units.

In [2]:

k_wood = 0.15 * watt / K / m
k_foam = 0.02 * watt / K / m

We define the thicknesses of the layers of wood and foam in the panel.

In [3]:

t_wood = 0.01 * m
t_foam = 0.14 * m

We can then calculate the R-values for the a wood layer and a foam layer.

In [4]:

r_wood = t_wood / k_wood
r_foam = t_foam / k_foam

The R-value is the sum of the layers. One wood, one foam, and then another wood layer.

In [5]:

r_SIP_SI = r_wood + r_foam + r_wood
r_SIP_SI

Out[5]:

We can multiply by a conversion factor to find the english R-value.

In [6]:

print(r_SIP_SI.magnitude * 5.68)

Out[6]:

40.5173333333

The software we are using allows the computer to convert between these units. We see the numbers agree to 4 significant figures.

In [7]:

r_SIP_SI.to(ft**2 * hour / BTU * F)

Out[7]:

We can also calculate the power lost by a large area of this wall.

Q = UA\Delta T = \frac{A \Delta T}{R_{total}}

In [8]:

length = 50 * m
height = 3 * m
t_inside = 20
t_outside = 5
height * length / r_SIP_SI * (t_inside - t_outside) * K

Out[8]: