Navier Stroke Equation (NSE) in the Transport Phenomena (Momentum, Heat, and Mass Transfer Balances) for the Movement of Water in A Horizontal Pipe from a Pumping Station to A Holding Facility Before Distribution

• Author(s): Dr. Adeola Grace Olugbenga ; Henry Akintola Akpa ; Amali Paul Elaine ; Oyelade Oluwabukoye Enoch ; Salihu Fatima Aliyu
• Paper ID: 1706866
• Page: 314-324
• Published Date: 13-01-2025
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 8 Issue 7 January-2025

Abstract

This study investigate the application of Navier Stokes equation in transport phenomenon, specifically examining water flow in horizontal pipe. The Navier-Stokes equations, which describe the mechanics of fluid motion, primarily control the flow behavior when water flows through horizontal pipes. These equations offer a mathematical model for explaining the motion of incompressible, viscous fluids and are derived from the basic ideas of mass, momentum, and energy conservation. The equations show the forces operating on the fluid, such as viscous forces, pressure gradients, and external body forces (if any, like gravity). Typically, in a horizontal pipe, the considerations are the cylindrical coordinates (r,?,z), where r is the radial distance, ? is the angular position, and z is the axial direction along the pipe. Velocity profile equation for laminar flow was used with assumed range of radial distance of r values from 0 (Centre) to R (pipe wall) to compute the velocity for each r in which the values obtained are tabulated and a plot of the velocity against radial distance demonstrating the inverse proportionality between them. The pipe radius R was used to calculate the volumetric flow rate Q and the data obtained was used to plot the graph of flowrate against pipe radius, The curve is steep and nonlinear, showcasing the R4 dependence. For a fixed pressure gradient and fluid viscosity, the flow rate increases exponentially as the pipe radius increase. The results highlight the significance of Navier Stokes equation in understanding and predicting fluid flow behavior in transport phenomenon.

Citations

IRE Journals:
Dr. Adeola Grace Olugbenga , Henry Akintola Akpa , Amali Paul Elaine , Oyelade Oluwabukoye Enoch , Salihu Fatima Aliyu "Navier Stroke Equation (NSE) in the Transport Phenomena (Momentum, Heat, and Mass Transfer Balances) for the Movement of Water in A Horizontal Pipe from a Pumping Station to A Holding Facility Before Distribution" Iconic Research And Engineering Journals Volume 8 Issue 7 2025 Page 314-324

IEEE:
Dr. Adeola Grace Olugbenga , Henry Akintola Akpa , Amali Paul Elaine , Oyelade Oluwabukoye Enoch , Salihu Fatima Aliyu "Navier Stroke Equation (NSE) in the Transport Phenomena (Momentum, Heat, and Mass Transfer Balances) for the Movement of Water in A Horizontal Pipe from a Pumping Station to A Holding Facility Before Distribution" Iconic Research And Engineering Journals, 8(7)