Annals of Civil Engineering and Management(ACEM)
ISSN: 3065-9779 | DOI: 10.33140/ACEM
Research Article - (2025) Volume 2, Issue 2
Analytical Solution for Fluid Dynamics
Received Date: Jun 07, 2025 / Accepted Date: Jul 16, 2025 / Published Date: Jul 24, 2025
Copyright: ©©2025 Paul T E Cusack. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation: Cusack, P. T. E. (2025). Analytical Solution for Fluid Dynamics, Ann Civ Eng Manag, 2(2), 01-06.
Abstract
In this important paper, we put fluid dynamics on a theoretic basis for some basic flows. We also put the Hazen Williams and Manning Equation on a theoretical foundation. Various other flow environments may be subject to similar transformations.
Introduction
Newtonian Fluids Low Viscosity
Teflon Mass = C2F4 = 2(12.011) + 4(18.989) = 99.989 x 6.022 = 602
∫1/2→π Ln t = 1.602
Mt-1 = M
M = t
PE = KE
PE-KE = 0 Conservation of Energy
t² - t - 1 = 0 GMP
F = Mα
(49989) (1/√2)
=35.3≈i
Figure 1: Cusack’s RLC Circuit
Figure 2: Cusack Exponential Mass-Time Plot
1533.5 x 2π/6.693 = 1/0.6946
15335-1.4645 = -0.0695
t = eM = e-0.0695 = 499 = V+
Hookes Law
σ = Yε
F/A = (0.4233) t
8/3 = 0.4233t
t = 1/0.1588 = 1/E
E = hν = ht6.628(1/0.1588)
=417
GMP: E=1/511=1/Me- flow of Electricity
sin² 45°+cos²45°= 1= x²/a²+y²/b²
θ=t=π/4
f 0 (x) = ax + 1-a
= 2x+1-2
= 2t-1 = dE/dt
dy/dx = a = f(x)″ = 2 = G
y = f0 (x) = ax + b = f(x)′
= 2x+b
= 2t-1
b = 1
For Laminar flow
Bernoulli
p + 1/2ρv² + z = 0
mgh + 1/2ρv² + 0 = 0
PE + KE = 0
M = t
E = 1- e -1
-1/t = 1-1/E
-1/t = 1-t
-1 = t -t²
t²- t -1 = 0 ⇒ GMP sheet flow
The GMP reigns for the flow out of a nozzle
Figure: 8 Source[1]
So, we’ve shown that the GMP is key to analyzing fluid dynamics theoretically
Hazen-Willimam for flow under pressure:
Hazen-Willimam for flow under pressure:
Note that turbulent flow is subject to the Fair Coin GMP Eqaution.
References
1.Meyer, RE. Introduction to Mathematical Fluid Dynamis. USA: Dover, 1971.