how to find D = 6.15 in part a ?

You are working for an engineering consulting company. A large oil company has hired your company to determine what diameter pipe to use to transport oil. The pipeline will handle 3.5 million barrels of oil per day, and the length of the pipeline will be 650 miles. The pipeline is expected to last 20 years with no salvage. The company installing the pipe wants to earn 10% on its money. The pumping power required =1,980,000(1,3330P) Horsepower where Q is the volume flow rate in cubic feet per hour and P is the pressure drop. Pressuredrop(P)=gD128QuLpoundspersquarefootg=417,312,000feethour2whereQisasgivenabove,uis8500poundsperhourfoot(oilviscosity),Lispipelinelengthinfeet,andDisinsidepipediameterinfeet. Electric power for the pumps will cost $0.02 per HP hour. The steel for the pipeline is $1.00 per pound of steel, and motor and pump costs are $210 per HP. Steel weighs 490.75 pounds per cubic foot. The thickness of the pipe is 0.015 of its inside diameter, D. Part a. Solve this problem analytically using the appropriate equations to determine the diameter of the pipe that results in the lowest annual equivalent cost (AEC) for the oil company. Construct a table showing how the AEC varies with diameter, from D=3ft to 10ft in .5ft increments. Construct another table showing how the optimal D varies with oil flow from 2.5 million barrels per day to 7 million barrels per day in .5 increments. You are working for an engineering consulting company. A large oil company has hired your company to determine what diameter pipe to use to transport oil. The pipeline will handle 3.5 million barrels of oil per day, and the length of the pipeline will be 650 miles. The pipeline is expected to last 20 years with no salvage. The company installing the pipe wants to earn 10% on its money. The pumping power required =1,980,000(1,3330P) Horsepower where Q is the volume flow rate in cubic feet per hour and P is the pressure drop. Pressuredrop(P)=gD128QuLpoundspersquarefootg=417,312,000feethour2whereQisasgivenabove,uis8500poundsperhourfoot(oilviscosity),Lispipelinelengthinfeet,andDisinsidepipediameterinfeet. Electric power for the pumps will cost $0.02 per HP hour. The steel for the pipeline is $1.00 per pound of steel, and motor and pump costs are $210 per HP. Steel weighs 490.75 pounds per cubic foot. The thickness of the pipe is 0.015 of its inside diameter, D. Part a. Solve this problem analytically using the appropriate equations to determine the diameter of the pipe that results in the lowest annual equivalent cost (AEC) for the oil company. Construct a table showing how the AEC varies with diameter, from D=3ft to 10ft in .5ft increments. Construct another table showing how the optimal D varies with oil flow from 2.5 million barrels per day to 7 million barrels per day in .5 increments