Q (ft3/min) : 3.9, 7.9, 11.8, 15.7, 19.6, 23.6, 27.5, 31.4, 35.3, 39.3
Delta P (psi): 0.13, 0.52, 1.18, 2.09, 3.27, 4.71, 6.41, 8.37, 10.59, 13.08
My professor gave the information above and wants us to come up with a linear equation that relates Q and square root of delta P. He also said that the pressure drop (delta P) is proportional to the flow rate squared (Q^2).
I have no idea how to come up with this equation please help or point me in the right direction.
He wants a linear equation like
q = k√p + n
where q = Q and p = psi
In fact, when he says that p is proportional to Q^2 it means that
p = q^2/k, so n=0
If you tabulate √p/.36 you will have
√p/.36 Q
1 3.9
2 7.9
3 11.8
4 15.7
5 19.6
6 23.6
7 27.5
8 31.4
9 35.3
10 39.3
Taking rounding into account, it looks like
Q = 3√p/.36
Q = 25/3 √p
or,
p = .36 q^2
Thank you so much.
When I tried your equations I did not receive the right values.
To come up with a linear equation that relates Q (flow rate) and the square root of delta P (pressure drop), we can use the information provided by your professor that the pressure drop is proportional to the flow rate squared.
Let's start by calculating the square root of delta P for each value and the corresponding flow rate squared (Q^2):
Square root of delta P:
√0.13 = 0.36
√0.52 = 0.72
√1.18 = 1.09
√2.09 = 1.45
√3.27 = 1.81
√4.71 = 2.17
√6.41 = 2.53
√8.37 = 2.89
√10.59 = 3.26
√13.08 = 3.62
Flow rate squared:
3.9^2 = 15.21
7.9^2 = 62.41
11.8^2 = 139.24
15.7^2 = 246.49
19.6^2 = 384.16
23.6^2 = 556.96
27.5^2 = 756.25
31.4^2 = 987.56
35.3^2 = 1246.09
39.3^2 = 1544.49
Now, let's plot these values on a graph, with √delta P on the x-axis and Q^2 on the y-axis.
Once the points are plotted, we can observe whether a linear relationship between √delta P and Q^2 exists. If there is a linear relationship, we can fit a straight line through the points.
If the points appear to be linearly related, you can use the method of least squares to find the equation of the best-fit line. This equation will represent the linear relationship between Q and the square root of delta P. The standard form of a linear equation is y = mx + b, where y is the dependent variable (Q^2), x is the independent variable (√delta P), m is the slope of the line, and b is the y-intercept.
By calculating the slope and y-intercept of the best-fit line, you will have the linear equation that relates Q and the square root of delta P.
Hope this helps!