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March 11, 2013

Fluid dynamic of drilling fluid (mud) through butterfly valve


The knowledge of fluid dynamics is crucial in both aerospace and thermodynamic engineering. In aerospace engineering, the knowledge is applied in the designing of aircraft wings for the proper air flow balance and manipulation of the various aircraft mobility position. In thermodynamics, fluid dynamics is used in the reticulation of the various fluids conduction through a pipe system (Gong, Ming, and Zhang, p 41 2011). The knowledge is also important in the generation of a specified amount of pressure in pressurized thermodynamic systems. A number of fluid dynamics computations and mechanisms are equally exploited in the design and management of the various thermodynamic systems. These computations and dynamics are subject to a number of fluid dynamics principles and equations derived by various fluids dynamic theorem. The fluid dynamics reticulation, power generation and control system mechanisms then exploits these fluid dynamic computation principles, theories and models to design and manage the various aerodynamic and fluid dynamic systems. This paper thus explores both the practicality of the various fluids dynamics principles and theories as demonstrated by the butterfly valve as a typical fluid dynamic reticulation system (Wesseling, 2009, p 884). The paper begins by defining and deriving the six principles and theorem of fluid dynamics and then proceeds to use those formulas and principles in the computation of pressure loss in a typical butterfly valve case sturdy. This realizes a successful demonstration of the fluid dynamic computation methodology in calculation of the pressure differentials in a typically isolated fluid dynamic system. It also shows the functional correlation between the design and reticulation component of a thermodynamic system on a fluid dynamic system. Lastly, the paper provides the functional mechanisms for influencing the pressure dynamics within a fluid dynamic system.

1. Conservation of Energy Turbulent and laminar.
The law of conservation of energy states that energy is neither created nor destroyed thus
the potential energy and kinetic energy of both a laminar and a turbulent flow in an isolated system must remain the same putting into account the energy dissipated in the system. According to the same principal, the total energy supplied to the isolated system in nature of the mechanical energy/work required for the flow of the fluid through the system is equal to the internal energy (kinetic and potential energy held by the flowing liquid) added to the system and the energy dissipated in course of the fluid flow in the system (Taylor, 2012, p 5983). On the other hand, the lamina or turbulent nature of the flow, which is characterized by the nature and uniformity/randomness of the flow, is determined by the internal energy held by the fluid flowing in the system. This internal energy is held as both kinetic and potential energy with the kinetic energy being functionally correlated to the flow velocity. Kinetic and potential energy of the fluid flowing in a system is related by the following equation.

p + (1/2)pv2

This is referred to as the Bernoulli equation. The equation demonstrates the functional correlation between pressure in an isolated system and the velocity of the fluid flow in the system. Velocity is also a function of the shear strain and stress on the fluid as it flows through a system from the viscosity drag between it and the wall of the system and amongst its individual particles. A high velocity coupled with a high viscosity drag is thus associated with a turbulent flow as large eddie current and recirculation results in a higher dissipation of the fluid particles internal energy. On the other hand, lamina flow is associated with less dissipation of internal energy, which is realized through a reduced velocity or frictional drag in the flow system. The law of conservation of energy is thus applicable in predicting a lamina or a turbulent flow in regard to the energy dynamics within a flow system in nature of the system design, fluid viscosity and reticulation velocity (Taylor, Controller design for nonlinear systems using the robust controller bode (RCBode) plot , 2011, p 1416).

The law of conservation of energy is expressed by the following equation.
vd + cdc + gdz + df = 0
Whereby df represents the energy losses attributed to the friction between the pipe internal surface and the fluid, gdz id the potential energy added to the fluid by the change in their position relative to an original datum position, cdc is the energy head attributed to the chemical potential of the fluid particles and vd is the energy attributed to the instantaneous velocity and pressure of the fluid.

2. Reynolds number.
Reynolds number gives a comparative ratio between a fluids viscosity and its forces of
inertia. This ratio is used to predict a turbulent or a lamina flow of the fluid with small Reynolds number value attributed to laminar flow while turbulent flows are associated with a Reynolds number that approaches an infinite value. Reynolds number also characterizes the viscosity and inertia forces of a fluid with inertia diminishing viscosity attributed to laminar flow whereas a viscosity diminishing inertia forces produce turbulent flows. The shape of the flow system internal surface area also plays a role in the laminar or turbulent flow of the fluid. In addition, the velocity of the fluid in the system determines the laminar or turbulent flow of the fluid and is also used in the calculation of Reynolds number. Reynolds number is thus used in modeling fluid flows dynamics under inertia, viscosity, velocity internal surface area/shape and velocity differential values (J. F. Gong, P. J. Ming, and W. P. Zhang, 2011, p 458).
The functional relationship between Reynolds number, viscosity and inertia forces is expressed by the following equation.

Re = (vL)/µ

Whereby Re is the Reynolds number,  denotes the fluid’s density, v is the surface/container/object relative velocity to the fluid’s velocity, L is the linear dimension travelled by the fluid and µ denotes the fluid’s dynamic viscosity.
The functional relationship between Reynolds number and the internal diameter of the system in which the fluid flows is expressed by the following equation.

Re = (vDH)/µ
Whereby Re is the Reynolds number,  is the fluids density, v is the fluid’s average velocity, DH represents the pipe’s hydraulic diameter and µ denotes the fluids dynamic viscosity.
The shape of the flow system is crucial in the calculation of the systems internal diameter/wetted perimeter together with its cross-sectional areas, which are used in the computation of the Reynolds coefficient. Regular systems such as squares and rectangles thus have a definite formula for the calculation of their hydraulic diameter, which is competed as

DH = 4A/P, where by A denotes the systems cross-sectional area and P is the wetted perimeter of the system or the perimeter around all the surfaces in contact with the fluid flowing in the system.
Irregular systems hydraulic diameter are computed using a number of individually derived computation formula,<…>

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