A brand of toothpaste is made using a mixture of white and red paste. During the manufacturing process, both pastes are pumped through a pipe, with the red paste lying in the centre of the pipe, as shown in Figure Q2. The pipe has an internal radius, R₂, and the segment of red paste has a radius R₁. The flow is found to follow the Poiseuille equation, i.e. 1 dp 4µ dx u(r) = -- (R2-r²) dx Where u is the viscosity of the paste and μ is the pressure gradient. The total flow of toothpaste through the pipe is Qtot, and the flowrate of the red paste is Qred. The toothpaste has a density of p = 1200 kg/m³, and a viscosity of 0.03 Pa.s. The pipe has a radius R₂ = 5 cm and a length L = 2 m. a) Find an expression for the flowrate of the red toothpaste. You answer should be in terms of µ, R₁, R₂, d) dp
A brand of toothpaste is made using a mixture of white and red paste. During the manufacturing process, both pastes are pumped through a pipe, with the red paste lying in the centre of the pipe, as shown in Figure Q2. The pipe has an internal radius, R₂, and the segment of red paste has a radius R₁. The flow is found to follow the Poiseuille equation, i.e. 1 dp 4µ dx u(r) = -- (R2-r²) dx Where u is the viscosity of the paste and μ is the pressure gradient. The total flow of toothpaste through the pipe is Qtot, and the flowrate of the red paste is Qred. The toothpaste has a density of p = 1200 kg/m³, and a viscosity of 0.03 Pa.s. The pipe has a radius R₂ = 5 cm and a length L = 2 m. a) Find an expression for the flowrate of the red toothpaste. You answer should be in terms of µ, R₁, R₂, d) dp
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Question 2
A brand of toothpaste is made using a mixture of white and red paste. During the
manufacturing process, both pastes are pumped through a pipe, with the red paste lying in
the centre of the pipe, as shown in Figure Q2. The pipe has an internal radius, R₂, and the
segment of red paste has a radius R₁. The flow is found to follow the Poiseuille equation,
i.e.
u(r) =
1 dp
4µ dx
(R₂-²)
dp
Where u is the viscosity of the paste and is the pressure gradient. The total flow of
toothpaste through the pipe is Qtot, and the flowrate of the red paste is Qred-
dx
The toothpaste has a density of p = 1200 kg/m³, and a viscosity of 0.03 Pa.s. The pipe
has a radius R₂ = 5 cm and a length L = 2 m.
a) Find an expression for the flowrate of the red toothpaste. You answer should be in
terms of µ, R₁, R₂, d)
dx
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