Final answer:
To calculate the flow speed of oil in a pipe with a given flow rate and diameter, we convert the flow rate to cubic meters per second, calculate the pipe's cross-sectional area, and then divide the flow rate by the area.
Step-by-step explanation:
The question asks us to calculate the speed at which oil with a density of 780 kg/m³ is flowing in a section of a pipe with a diameter of 8.0 cm when the flow rate is 8 L/s. To find the flow speed, we first convert the flow rate from liters per second to cubic meters per second (since 1 L = 0.001 m³, then 8 L/s becomes 0.008 m³/s). Next, we use the formula Q = A*v, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the flow speed.
To find the area A, we use the formula for the area of a circle, A = π*(d/2)^2, where d is the diameter of the pipe. In this case, d = 0.08 m (since 8.0 cm = 0.08 m). Substituting the values, we can calculate A and solve for the flow speed v using the rearranged equation v = Q/A. This will give us the speed at which the oil flows through that section of the pipe.
Remember, the mass flow rate (pAv) should be the same throughout the pipe, assuming a constant density of the oil.