Stating and Deriving Bernoulli’s Theorem as a Special Case of Steady Flow Energy Equation

2021 ◽  
pp. 217-225
Author(s):  
Abhishek David ◽  
Annu Kumar Lakshya ◽  
Mona sahu ◽  
Rahul Kumar Sinha
Thermofluids ◽  
1996 ◽  
pp. 25-27
Author(s):  
Keith Sherwin ◽  
Michael Horsley
Keyword(s):  

2009 ◽  
Vol 19 (09) ◽  
pp. 2939-2951 ◽  
Author(s):  
JACQUES HONA ◽  
ELISABETH NGO NYOBE ◽  
ELKANA PEMHA

In this paper, the axisymmetric flow of a viscous fluid through a porous annular tube with walls kept at different temperatures is studied theoretically. The physical properties of the fluid remain constant, notably its specific mass, its dynamic viscosity and its thermal diffusivity. The nondimensional parameters which the solutions of the problem depend on are defined. A numerical integration using the shooting method is applied for solving the Navier–Stokes equations and the energy equation. Bifurcation diagrams are presented and enable to highlight significant properties of the flow. Some thermal behaviors corresponding to specific values of the parameters are performed. Asymmetric solutions of the steady flow are described and some results about velocity components are also analyzed.


Author(s):  
А. А. Тkachev ◽  
◽  
А. М. Аnokhin ◽  

Purpose: checking the headrace canal to the fall no. 1 for diversion capacity in connection with a change in the canal discharge. Due to the increase in the estimated flow for irrigation and watering, it is planned to build a canal from the reservoir to the fall no. 1. The tasks of the hydraulic computation included the determining of the headrace canal parameters for the intended catastrophic water discharge of 375 cubic m/s, the computation was carried out taking into account the non-steady flow in canal. For effective energy extinction in the tail-race of the fall, it is required to make a constructive decision and carry out a justification taking into account the topographic conditions of the structure's operation. It is necessary to resolve the issue of energy extinction in tail-race of the structure. Calculations of the toothed overfall for energy extinction in the tail-race are presented. Materials and methods. A version of the dissipator with an indented wall which allows dissipate energy in the constraint environment effectively and obtain a favorable distribution of velocities in the flow in tail race of the structure was adopted for the computation. A step-by-step computation for determining the diversion capacity of the fall no. 1 was carried out: first, the diversion capacity of the headrace canal was determined at a catastrophic discharge Q = 375 cubic m/s with a subsequent change in its hydraulic parameters, then the computation for dissipating the flow energy in the downstream of the structure are given. Results: the calculations of the jagged sill for damping the energy in the tail-race are presented, the indented wall of the fall is designed and the corresponding depths in the tail-race are calculated. Conclusions: the performed computation of the headrace canal and fall no. 1 made it possible to ensure the passage of a catastrophic flow rate equal to 375 cubic m/s, under set conditions.


Thermofluids ◽  
1996 ◽  
pp. 29-31
Author(s):  
Keith Sherwin ◽  
Michael Horsley
Keyword(s):  

Author(s):  
M. R. Abbott ◽  
M. J. Lighthill

ABSTRACTA theory is presented of the non-linear propagation of waves and bores in channels of varying cross-section with a basic steady flow governed by frictional resistance; this corresponds to the flow in tidal rivers. The theory provides a condition on the tidal range required to produce a bore, in terms of the geometry and friction parameters of the river, and the propagation of such a bore is then described. The theory is applied to the River Severn and the results agree satisfactorily with observation. The results for the special case of waves moving into still water in a channel of varying section are also noted in detail.


Thermofluids ◽  
1996 ◽  
pp. 137-152
Author(s):  
Keith Sherwin ◽  
Michael Horsley
Keyword(s):  

2020 ◽  
pp. 116-122
Author(s):  
A.P. GURYEV ◽  
◽  
B.A. HAEK ◽  

The aim of the work is to analyze the existing method of calculating the spillway from the depth of the free flow under uneven mode in prismatic channels with a slowly changing movement and to develop a method of calculations that allows applying it to any flows in a prismatic channel without using any special tables. The existing methods for calculating flow parameters are based on the use of the Chesy formula to determine the flow consumption with a slowly changing water movement. At the same time, there is a V.I. Charnomsky’s method of direct calculation of the flow parameters from the energy equation without limiting the value of the channel slope. The disadvantage of this method is a possibility to solve the energy equation by the method of sequential approximation since the flow energy equation includes two variables, the flow depth and the distance between the sections. To eliminate this difficulty, it is proposed to determine the distance between the depths that make up the geometric progression on the considered part of the channel which allows calculating parameters of the free fl ow surface for any channel slopes and hydraulic flow modes without to special tables.


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