Givens: D(in)= 13 SigD(in) 0.0455 S(%)= 3.90 SigS(%)= 0.42 n= 0.012 SigN=0.0043

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Givens: D(in)= 13 SigD(in) 0.0455 S(%)= 3.90 SigS(%)= 0.42 n= 0.012 SigN=0.0043
Please provide all steps and calculations
Thanks! Givens: D(in)= 13 SigD(in) 0.0455 S(%)= 3.90 SigS(%)= 0.42 n= 0.012 SigN=0.0043
Please provide all steps and calculations
Thanks! 2 1.4859 R S 0.5, where V is ft/s, R in ft, and V = Sin ft/ft. However, in the US pipes are commonly specified by their diameter expressed in inches, and S is expressed in percentage ie. 1% for 0.01. The resulting equation is 72 1.4859( DNG)( s 0.5 and Q Vr(-) 2, Q is in ft3/s or cfs. 7n 100 24 Compute the standard deviation of the velocity and flow rate based on the data provided. If the units of n are seconds/m, the constant's units are (ft/my/s. Also discuss which variables uncertainties are most influential.

Explanation / Answer

Given
V = (1.4859/n)(D/48)^2/3 * (s/100)^0.5
Q = V*pi(D/24)^2

D = 13 in
d(D) = 0.0455

S = 3.9
d(s) = 0.42

n = 0.012
d(n) = 0.0043

so, V = (1.4859/0.012)(13/48)^2/3 * (3.9/100)^0.5 = 10.2362
Q = V*pi(13/24)^2 = 9.435 ft^3/s

and dQ/Q = sqroot(((8/3)dD/D)^2 + (0.5dS/S)^2 + (dn/n)^2)
dQ/9.435 = sqroot(((8/3)*0.0455/13)^2 + (0.5*0.42/3.9)^2 + (0.0043/0.012)^2)
dQ= 3.4199 ft^3/s

so the most influential uncertianity will be uncertianinty in D

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