Navier-Stokes, Cylindrical. Water flows in a vertical pipe of radius R = 2 cm. In the coordinates shown: (a) solve for V(r) in terms of dp/dz, μ, R, p, and g. (b) evaluate the flow rate down the pipe if dp/dz = 0; (c) evaluate the minimum value of dp/dz needed to stop the flow from going down the pipe?; (d) what value of dp/dz is required to have the flow go up the pipe at the same as the flow rate down in part 'b' ? ; (e) what is the centerline (r = 0) speed for each of the conditions (i.e. dp/dz) in each of b,c,d? Units for expecting: (a) Vz = C1 [r^2 /R^2 - 1]; (b) Q: 10^-1 m^3/s; (c) dp/dz,stop: 10^3 Pa/m; (d) dp/dz,up: 10^4 Pa/m; (e) Vb = 10^2 m/s; Vc = 10^0 m/s ; Vd = -10^2 m/s SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; μwater - 10^-3 N•s/m^2; pair - 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2 R
Navier-Stokes, Cylindrical. Water flows in a vertical pipe of radius R = 2 cm. In the coordinates shown: (a) solve for V(r) in terms of dp/dz, μ, R, p, and g. (b) evaluate the flow rate down the pipe if dp/dz = 0; (c) evaluate the minimum value of dp/dz needed to stop the flow from going down the pipe?; (d) what value of dp/dz is required to have the flow go up the pipe at the same as the flow rate down in part 'b' ? ; (e) what is the centerline (r = 0) speed for each of the conditions (i.e. dp/dz) in each of b,c,d? Units for expecting: (a) Vz = C1 [r^2 /R^2 - 1]; (b) Q: 10^-1 m^3/s; (c) dp/dz,stop: 10^3 Pa/m; (d) dp/dz,up: 10^4 Pa/m; (e) Vb = 10^2 m/s; Vc = 10^0 m/s ; Vd = -10^2 m/s SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; μwater - 10^-3 N•s/m^2; pair - 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2 R
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![Navier-Stokes, Cylindrical. Water flows in a vertical pipe of radius R = 2 cm. In the coordinates shown: (a) solve for V(r) in terms of dp/dz, μ, R, p, and g. (b)
evaluate the flow rate down the pipe if dp/dz = 0; (c) evaluate the minimum value of dp/dz needed to stop the flow from going down the pipe?; (d) what
value of dp/dz is required to have the flow go up the pipe at the same as the flow rate down in part 'b' ? ; (e) what is the centerline (r = 0) speed for each
of the conditions (i.e. dp/dz) in each of b,c,d?
Units for expecting: (a) Vz = C1 [r^2/R^2 - 1]; (b) Q: 10^-1 m^3 /s; (c) dp/dz,stop: 10^3 Pa/m; (d) dp/dz,up: 10^4 Pa/m; (e) Vb = 10^2 m/s; Vc = 10^0 m/s ;
Vd = -10^2 m/s
SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; μwater - 10^-3 N•s/m^2; pair ~ 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2
R
Aft](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff46cd712-1d53-471c-8e4d-5e78c3c80932%2Fa147cc57-cfb9-401c-a156-992b0c17b626%2Fhkzs4f9_processed.png&w=3840&q=75)
Transcribed Image Text:Navier-Stokes, Cylindrical. Water flows in a vertical pipe of radius R = 2 cm. In the coordinates shown: (a) solve for V(r) in terms of dp/dz, μ, R, p, and g. (b)
evaluate the flow rate down the pipe if dp/dz = 0; (c) evaluate the minimum value of dp/dz needed to stop the flow from going down the pipe?; (d) what
value of dp/dz is required to have the flow go up the pipe at the same as the flow rate down in part 'b' ? ; (e) what is the centerline (r = 0) speed for each
of the conditions (i.e. dp/dz) in each of b,c,d?
Units for expecting: (a) Vz = C1 [r^2/R^2 - 1]; (b) Q: 10^-1 m^3 /s; (c) dp/dz,stop: 10^3 Pa/m; (d) dp/dz,up: 10^4 Pa/m; (e) Vb = 10^2 m/s; Vc = 10^0 m/s ;
Vd = -10^2 m/s
SI constant Patm = 10^5 Pa; pwater ~ 1000 kg/m^3; pair - 1.2kg/m^3; μwater - 10^-3 N•s/m^2; pair ~ 2 x 10^-5 N•s/m^2; g = 9.8 m/s^2
R
Aft
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