Final answer:
This is a related rates problem involving the addition of sand to a conical pile at a given rate. We need to calculate the resistance of the hose, the viscosity of the concrete, and the power being supplied.
Step-by-step explanation:
In this problem, we are given the flow rate of concrete being pumped through a hose and asked to calculate the resistance of the hose, the viscosity of the concrete, and the power being supplied. Here's how we can solve each part:
(a) Calculate the resistance of the hose:
The resistance of the hose can be calculated using the formula R = τL/A, where R is the resistance, τ is the viscosity, L is the length of the hose, and A is the cross-sectional area of the hose.
(b) Determine the viscosity of the concrete:
The viscosity of the concrete can be found using the formula τ = (PR)/(QV), where τ is the viscosity, P is the pressure at the pump, R is the resistance of the hose, Q is the flow rate, and V is the volume of the concrete.
(c) Calculate the power being supplied:
The power being supplied can be calculated using the formula P = QτH, where P is the power, Q is the flow rate, τ is the viscosity, and H is the height at which the concrete is being pumped.