Final answer:
To find the volume flow rate of petroleum and the diameter of the pipe at the refinery, we apply the principle of conservation of mass. By using the given flow speeds and the diameter at the wellhead, the volume flow rate is calculated, and the diameter at the refinery is determined using the continuity equation.
Step-by-step explanation:
The question asks to determine the volume flow rate (Q) of the petroleum in a pipe system and the diameter (d) of the pipe at the refinery given the flow speed changes from 11.1 m/s at the wellhead to 6.67 m/s at the refinery, and the diameter at the wellhead is 0.585 meters.
To calculate the volume flow rate, we use the equation Q = A * v, where A is the cross-sectional area of the pipe and v is the flow speed. Since at the wellhead the diameter is 0.585 m, we can calculate its area using the formula A = (π/4)*D². By knowing the flow rate is constant throughout the pipe, we can use the initial flow rate to find the flow rate at the refinery, and with the new flow speed given, we can then find the new diameter of the pipe.
First, let's calculate the area at the wellhead:
A₁ = (π/4) * (0.585 m)²
Then we multiply by the flow speed to find Q:
Q = A₁ * 11.1 m/s = (π/4) * (0.585 m)² * 11.1 m/s
Using Q and the flow speed at the refinery, we can calculate the diameter at the refinery (D₂) using the continuity equation for Q.
Q = A₂ * 6.67 m/s = (π/4) * D₂² * 6.67 m/s
Solving for D₂ we can find the diameter of the pipe at the refinery.