1. An engineer needs to know the flow rate through a 60″ (5-ft) water pipe, given its Hazen-Williams roughness coefficient C=100 on a 1% hydraulic grade.

The Hazen-Williams equation for determining the flow rate in a water pipe is:

Q = 1.318CR2.63S0.54 Where Q is the flow rate (ft3 /sec); R is the hydraulic radius (ft); C is the coefficient of roughness; and S is the hydraulic gradient (ft/ft).

1(a) What flow rate will the pipe deliver? …………………………………………Ans: Q = 756 ft3 /sec

Upon further discussion with the manufacturer, the engineer learns that the C factor for this pipe is normally distributed with a mean of 100 and a standard deviation of 12. The hydraulic radius is uniformly distributed between 4.8 and 5.2. Run a Monte Carlo simulation of this pipe with at least 1,000 trials, to determine the simulated flow rates and create a frequency plot of the results.

1(b) Generally, how are the results of this simulation distributed? Where does the original flow rate fall within this distribution? How confident should you be that the pipe will deliver a flow rate as originally calculated? Calculate the flow exceedance probability from your simulation.

1(c) What is the approximate probability that the actual flow will meet or exceed your calculated flow? Ans: About 30-35%

1(d) If you are required to exceed a 90% confidence threshold in your results, what flow rate would you report for this pipe? …………………………………………………..Ans: Q = 550-600 ft3 /sec 

If anyone can help me to solve this problem using excel spreadseet.