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C4.1 In a certain medical application, water at room temperature and pressure flows through length cm, and b-0.3 mm. The volume flow is sinusoidal, with amplitude Qo - 0.5 ml/s and frequency f-20 Hz, that is. Q- Qusin(2.7ft). (a) Calculate the maximum Reynolds number Re - Vb/v, based on maximum average velocity and gap thickness. Channel flow remains laminar for Re <2000, otherwise it will be turbulent. Is this flow laminar or turbulent? (b) Assume quasi-steady flow, that is, solve as if the flow were steady at any given Q(1). Find an expression for streamwise velocity # as a function of y. 8. dp/dx. and b, where dp/dx is the pressure gradient required to drive the flow through the channel at flow rate Q. Also estimate the maximum magnitude of velocity component u. (c) Find an analytic expression for flow rate Q(t) as a function of dp/dx. (di Estimate the wall shear strass ne o function of fuhs and time t.

C4.1 In a certain medical application, water at room temperature and pressure flows through length cm, and b-0.3 mm. The volume flow is sinusoidal, with amplitude Qo - 0.5 ml/s and frequency f-20 Hz, that is. Q- Qusin(2.7ft). (a) Calculate the maximum Reynolds number Re - Vb/v, based on maximum average velocity and gap thickness. Channel flow remains laminar for Re <2000, otherwise it will be turbulent. Is this flow laminar or turbulent? (b) Assume quasi-steady flow, that is, solve as if the flow were steady at any given Q(1). Find an expression for streamwise velocity # as a function of y. 8. dp/dx. and b, where dp/dx is the pressure gradient required to drive the flow through the channel at flow rate Q. Also estimate the maximum magnitude of velocity component u. (c) Find an analytic expression for flow rate Q(t) as a function of dp/dx. (di Estimate the wall shear strass ne o function of fuhs and time t.

Introduction to Chemical Engineering Thermodynamics
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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COMPREHENSIVE PROBLEMS C4.1 In a certain medical application, water at room temperature and pressure flows through a rectangular channel of length L = 1 and thickness b-0.3 mm. The volume flow is sinusoidal, with amplitude Qo= 0.5 ml/s and frequency f-20 Hz, that is. Q- Qasin(27f (). (a) Calculate the maximum Reynolds number Re Vb/v, based on maximum average velocity and gap thickness. Channel flow remains laminar for Re < 2000, otherwise it will be turbulent. Is this flow laminar or turbulent? (b) Assume quasi-steady flow, that is, solve as if the flow were steady at any given Q(1). Find an expression for streamwise velocity u as a function of y. u. dp/dx. and b. where dp/dx is the pressure gradient required to drive the flow through the channel at flow rate Q. Also estimate the maximum magnitude of velocity component ". (c) Find an analytic expression for flow rate Q(t) as a function of dp/dx. (d) Estimate the wall shear stress Tw as a function of Q. f, ut, b, s, and time 1. (e) Finally, use the given numbers to estimate the wall shear amplitude, Two, in Pa.
Transcribed Image Text:COMPREHENSIVE PROBLEMS C4.1 In a certain medical application, water at room temperature and pressure flows through a rectangular channel of length L = 1 and thickness b-0.3 mm. The volume flow is sinusoidal, with amplitude Qo= 0.5 ml/s and frequency f-20 Hz, that is. Q- Qasin(27f (). (a) Calculate the maximum Reynolds number Re Vb/v, based on maximum average velocity and gap thickness. Channel flow remains laminar for Re < 2000, otherwise it will be turbulent. Is this flow laminar or turbulent? (b) Assume quasi-steady flow, that is, solve as if the flow were steady at any given Q(1). Find an expression for streamwise velocity u as a function of y. u. dp/dx. and b. where dp/dx is the pressure gradient required to drive the flow through the channel at flow rate Q. Also estimate the maximum magnitude of velocity component ". (c) Find an analytic expression for flow rate Q(t) as a function of dp/dx. (d) Estimate the wall shear stress Tw as a function of Q. f, ut, b, s, and time 1. (e) Finally, use the given numbers to estimate the wall shear amplitude, Two, in Pa.
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