Comparison of Adam’s Bashforth Method and Finite Difference Method
- May 12, 2018
- Posted by: RSIS
- Category: Civil Engineering
International Journal of Research and Scientific Innovation (IJRSI) | Volume V, Issue IV, April 2018 | ISSN 2321–2705
Comparison of Adam’s Bashforth Method and Finite Difference Method
Dr. Birendra Kumar Singh
Civil Engineering Department, Birla Institute of Technology, Mesra, Ranchi-835215 (Jharkhand), India
Abstract: – The comparison between Adam’s Bashforth method and Finite difference method is done for double differential equation of mean depth of flow and mean velocity of flow. It is found that Finite difference method is more appropriate because the mean velocity of flow y2 = 0.640 m/sec = Mean velocity found by Finite difference method which is nearly equal to the value obtained by table of 0.75-inch roughness bed data (provided in the section – Observation tables in the manuscript). On the basis of y2 determined, the corresponding value of discharge of flow is found from table of 0.75-inch roughness bed data and discharge of flow for river hydraulics is found and hence thickness of stone pitching, thickness of apron and scoured depth are determined.
Keywords: Mean velocity of flow, Mean depth of flow, Finite difference method, Adam’s Bashforth method, Differential equation
I. INTRODUCTION
The mean velocity is related to mean depth of flow with respect to average value and analysis is done with respect to Adam’s Bashforth Method and Finite difference method taking double differential equation. And it is seen that finite difference method is more appropriate method as compared to Adam’s Bashforth Method.
II. EXPERIMENTAL SETUP & PROCEDURES
Flume Data were obtained for 0.75-inch roughness bed.
Flume: -The flume is open and it is 1.168m wide and 9.54m long. Roughness bed was obtained by smearing masonite boards with fiberglass resin. The boards were screwed to the bed of the flume.
Experimental Procedure: -Five to seven flows were taken for three different slopes (2, 5 and 8%). At each flow, depth was measured at a single cross section, so that channel properties could be calculated.
