Here is my equation in which I am trying to calculate the uncertainty in a measu

Question

Here is my equation in which I am trying to calculate the uncertainty in a measurement of the coefficient of skin friction of turbulent flow through a large pipe. In the equation, I am actually measuring with sensors the velocity of the flow (V), the diameter of the pipe (D), and the temperature (T) and pressure (P) of the flow. Density is calculated as a function of temperature and pressure. It is worth noting that the working fluid of the analysis is water.  

Here are the nominal values and their respective uncertainties:

V = 2 m/s

D = 1 m

T = 450 K

P = 7 MPa

uncertainty in V = +/- 0.02 m/s

uncertainty in D = +/- 0.001 mm

uncertainty in T = +/- 0.6 K

uncertainty in P = +/- 0.0175 MPa

Also worth noting is that the nested expression:

has an uncertainty associated with it as well of +/- 2.5 %

Here, density (rho) is given as a function of temperature and pressure and will likewise have an uncertainty associated with it as well.

I need to calculate the total uncertainty in the coefficient of skin friction Cf for which the equation is solved for.

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Here is my equation in which I am trying to calculate the uncertainty in a measu

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