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Water is in steady fully developed laminar flow between two horizontal, very wide (W) and long (L) parallel surfaces separated by a distance b. The bottom surface at y = 0 moves in the negative x-direction at a speed vo while the top surface at y = b is stationary. In addition, a constant pressure gradient dP/dx is acting on the liquid in the x-direction. (a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions. (b) Derive an equation for the velocity profile in terms of the parameters, dP/dx, b, vo and µ. (c) Obtain an equation for the volumetric flow rate. (d) Assume that water has a density p = 1000 kg/m³ and viscosity u = 1.0 x 10-³ kg/m-s. If the pressure gradient is dP/dx = -1.5 Pa/m, b = 6 mm, W = 1.0 m, and the speed of the bottom surface is 1.0 cm/s, calculate the volumetric flow rate of water and specify the direction of flow (positive or negative x-direction).

Water is in steady fully developed laminar flow between two horizontal, very wide (W) and long (L) parallel surfaces separated by a distance b. The bottom surface at y = 0 moves in the negative x-direction at a speed vo while the top surface at y = b is stationary. In addition, a constant pressure gradient dP/dx is acting on the liquid in the x-direction. (a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions. (b) Derive an equation for the velocity profile in terms of the parameters, dP/dx, b, vo and µ. (c) Obtain an equation for the volumetric flow rate. (d) Assume that water has a density p = 1000 kg/m³ and viscosity u = 1.0 x 10-³ kg/m-s. If the pressure gradient is dP/dx = -1.5 Pa/m, b = 6 mm, W = 1.0 m, and the speed of the bottom surface is 1.0 cm/s, calculate the volumetric flow rate of water and specify the direction of flow (positive or negative x-direction).

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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Water is in steady fully developed laminar flow between two horizontal, very wide (W) and long (L) parallel surfaces separated by a distance b. The bottom surface at y = 0 moves in the negative x-direction at a speed v. while the top surface at y = b is stationary. In addition, a constant pressure gradient dP/dx is acting on the liquid in the x-direction. (a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions. (b) Derive an equation for the velocity profile in terms of the parameters, dP/dx, b, v, and µ . (c) Obtain an equation for the volumetric flow rate. (d) Assume that water has a density p= 1000 kg/m' and viscosity u is dP/dx = -1.5 Pa/m, b = 6 mm, volumetric flow rate of water and specify the direction of flow (positive or negative x-direction). 1.0 x 10-3 kg/m's. If the pressure gradient 1.0 m, and the speed of the bottom surface is 1.0 cm/s, calculate the W
Transcribed Image Text:Water is in steady fully developed laminar flow between two horizontal, very wide (W) and long (L) parallel surfaces separated by a distance b. The bottom surface at y = 0 moves in the negative x-direction at a speed v. while the top surface at y = b is stationary. In addition, a constant pressure gradient dP/dx is acting on the liquid in the x-direction. (a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions. (b) Derive an equation for the velocity profile in terms of the parameters, dP/dx, b, v, and µ . (c) Obtain an equation for the volumetric flow rate. (d) Assume that water has a density p= 1000 kg/m' and viscosity u is dP/dx = -1.5 Pa/m, b = 6 mm, volumetric flow rate of water and specify the direction of flow (positive or negative x-direction). 1.0 x 10-3 kg/m's. If the pressure gradient 1.0 m, and the speed of the bottom surface is 1.0 cm/s, calculate the W
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