Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 250 L/min through a 50.0 m long, 8.00 cm diameter hose, and the pressure at the pump is 8.50 ✕ 106 N/m2 (about 1200 psi).

(a) Calculate the resistance of the hose.
(b) What is the viscosity of the concrete, assuming the flow is laminar?
(c) How much power is being supplied, assuming the point of use is at the same level as the pump? You may neglect the power supplied to increase the concrete's velocity.

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(a) To calculate the resistance of the hose, we need to determine the flow rate and pressure drop across the hose. The resistance of a hose can be calculated using Poiseuille's law, which states that the resistance is given by R = (8ηL) / (πr^4), where η is the viscosity of the fluid (in this case, concrete), L is the length of the hose, and r is the radius of the hose.

First, let's convert the diameter of the hose to radius:
radius = diameter / 2 = 8.00 cm / 2 = 4.00 cm = 0.04 m

Given:
Flow rate (Q) = 250 L/min = 250/60 m^3/s
Length of the hose (L) = 50.0 m
Radius of the hose (r) = 0.04 m

Using Poiseuille's law, we can calculate the resistance (R) of the hose:
R = (8ηL) / (πr^4)

Next, we need to determine the pressure drop (ΔP) across the hose. The pressure drop is given by ΔP = P1 - P2, where P1 is the pressure at the pump and P2 is the pressure at the point where concrete is being laid.

Given:
Pressure at the pump (P1) = 8.50 x 10^6 N/m^2
Assuming atmospheric pressure at the point of use, P2 = 1.01 x 10^5 N/m^2 (standard atmospheric pressure)

Using the above values, we can calculate the resistance of the hose (R) as follows:
R = (P1 - P2) / Q

Substituting the values we have:
R = (8.50 x 10^6 N/m^2 - 1.01 x 10^5 N/m^2) / (250/60 m^3/s)

(b) To determine the viscosity of the concrete, we can rearrange Poiseuille's law to solve for η:
η = (Rπr^4) / (8L)

Using the calculated values of R, r, and L, we can calculate the viscosity (η) of the concrete.

(c) To calculate the power being supplied, we can use the formula:
Power (P) = ΔPQ,

where ΔP is the pressure drop across the hose and Q is the flow rate.

Substituting the values we have, we can calculate the power being supplied.