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Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 200 L/min through a 50.0-m-long, 8.00-cm-diameter hose, and the pressure at the pump is

8.00×106N/m2.
(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.

2 Answers

7 votes

Final answer:

(a) The resistance of the hose is 8.00 × 10
^11 N s
^2/m
^5.

(b) The viscosity of the concrete, assuming laminar flow, is 400 Pa s.

(c) The power being supplied, neglecting the power to increase velocity, is 256 kW.

Explanation:

(a) To determine the resistance of the hose, we can use the Hagen-Poiseuille equation for flow through a cylindrical pipe:
\(R = (8 \eta L)/(\pi r^4)\), where \(R\) is the resistance,
\(\eta\) is the viscosity,
\(L\) is the length of the hose, and
\(r\) is the radius. Given the length
\(L = 50.0 \, \text{m}\), diameter
\(d = 8.00 \, \text{cm}\), and pressure
\(P = 8.00 * 10^6 \, \text{N/m}^2\), we find the radius
\(r\) and then calculate the resistance
\(R\).

(b) For laminar flow, the Hagen-Poiseuille equation can be rearranged to solve for viscosity:
\(\eta = (R \pi r^4)/(8L)\). Substituting the known values, including the resistance calculated in part (a), we find the viscosity
\(\eta\).

(c) To find the power supplied, we can use the formula
\(P = Q \Delta P\), where \
(P\) is power, \(Q\) is the flow rate, and
\(\Delta P\) is the pressure difference. Given the flow rate
\(Q = 200 \, \text{L/min}\) and pressure
\(8.00 * 10^6 \, \text{N/m}^2\), we convert the flow rate to
\(3.33 * 10^(-3) \, \text{m}^3/\text{s}\) and calculate the power supplied by the pump.

User Brian Riehman
by
5.2k points
3 votes

Answer:

a. 2.4 ×109 N ⋅ m2/s

b. 48.3 N⋅s /m2

c. 8.00×104W

Step-by-step explanation:

See Attached file for explanation

Concrete is pumped from a cement mixer to the place it is being laid, instead of being-example-1
Concrete is pumped from a cement mixer to the place it is being laid, instead of being-example-2
Concrete is pumped from a cement mixer to the place it is being laid, instead of being-example-3
User Nitin Bisht
by
5.8k points