3.5.3 Fanning Friction Factor (fw) Determination The fanning friction factor, fw is a function of the flow Reynolds’ number. It is required for calculating the contribution of frictional force to the momentum equation (equation (3.28)). In the developed UCL model, the Chen (Chen, 1979) correlation is employed for the calculation of the fanning friction factor for transition and turbulent flows in rough pipes. It is given by: 1/√(f_w )=3.48-1.7372 ln[ε/r_in -16.2446/Re lnA ] (3.76) Where A= [ε⁄r_in ]^1.0198/6.0983+ (7.149/Re)^0.8981 (3.77) ε, is the pipe roughness and rin represents the pipe inner radius. 3.6. The Steady State Isothermal Flow Model (Existing UCL Model) In this section, the steady state isothermal flow model developed by Atti (2006) and Garfield (2009) is presented. The model is for one-dimensional flow based on the continuity and momentum equations presented in section 3.2.1 and 3.2.2 respectively. From equation (3.6), the steady state expression (i.e. when all fluid properties are time invariant) for continuity in one-dimension can be written as: u ∂ρ/∂x+ ρ ∂u/∂x=0 (3.78) The author derived the single-phase and two-phase isothermal steady state flow equations based on isothermal flow assumption. 3.6.1 Single-phase isothermal steady state flow equations Due to the isothermal flow assumption, only the continuity together with the momentum or energy equation is required for the complete solution of the steady state problem. For single-phase flow, the conti... ... middle of paper ... ... Eng., 58, 122-123, 1980. Schlichting, H., “Boundary-Layer Theory”, McGraw-Hill, New York, 1979 Swameer, P. K. and Jain, A. K., “Explicit equation for pipe flow problems”, Journal on Hydr.Divi., ASCE, 102 (5), 657-664, 1976. The American Gas Association, Distribution-System Design, AGA Arlington 1990. United States of America Department of Transportation – Office of Pipeline Safety. http://ops.dot.gov/stats/stats.htm Wood, D. J., “An Explicit friction factor relationship” Civil Eng., 60-61, 1996 Von Bernuth, R. D., and Wilson T., “Friction Factors for small diameter plastic pipes” Journal Hydraulics Eng. 115 (2), 183-192, 1989. Zaragola, M. V., “Mean-flow scaling of Turbulent Pipe Flow” PhD thesis, Princeton University, USA, 1996. Zigrang, D. J. and Sylvester, N. D., “Explicit approximations to the Colebrook’s friction factor”, AICHE Journal 28, 3, 514, 1982
Two equations were used in this experiment to determine the initial temperature of the hot water. The first equation
The results collected during this investigation were as follows: 68.4 dB for the 10 cm pipe, 69.8 dB for the 20 cm pipe, 79 dB for the 30 cm pipe, 84.2 dB for the 40 cm pipe, and 84.2 dB for the 50 cm pipe. The hypothesis states: if the length of the PVC pipes were to increase and the frequency used in this experiment remained the same, then the sound produced from the pipe will have a lower amplitude each time. According
"As a rule of thumb R< ~2000 laminar flow and R> ~3000 turbulent flow" Anything in between 2000 and 3000 is unstable and may go back and forth between laminar and turbulent flow.
In classical fluid dynamics, the Navier-Stokes equations for incompressible viscous fluids and its special (limiting) case the Euler equations for inviscid fluids are sets of non-linear partial differential equations that describes the spatiotemporal evolution of a fluid (gas). Both equations are derived from conservative principles and they model the behavior of some macroscopic variables namely: mass density, velocity and temperature.
The distances on the inclined plane (s1 = 1.5m) and tabletop (s2 = 4.0m) were chosen to make the error margin smaller. By making these distances longer, the affect of friction was larger; however this effect is relatively small. Shorter distances would have resulted in large error margins; therefore it was beneficial to have longer inclined plane and tabletop distances.
The shear viscosity is a transport coefficient for momentum in inhomogeneous flows. This transport coefficient, which is widely used to describe both plasmas and fluids, relates two hydrodynamic quantities: shear stress and shear rate. The shear stress Pxy is the off-diagonal element of a pressure tensor, and the shear rate γ is the transverse gradient of the flow velocity u. For a flow in the y direction,
Introduction to Aerodynamics Aerodynamics is the study of the motion of fluids in the gas state and bodies in motion relative to the fluid/air. In other words, the study of aerodynamics is the study of fluid dynamics specifically relating to air or the gas state of matter. When an object travels through fluid/air there are two types of flow characteristics that happen, laminar and turbulent. Laminar flow is a smooth, steady flow over a smooth surface and it has little disturbance. Intuition would lead to the belief that this type of air flow would be desirable.
Refrigeration, the production of cold, is an essential practice for present-day living. It is used in a many place like the processing and preservation of food, conditioning of air for comfort, manufacture of chemicals and other materials, cooling of concrete, medical applications etc. Refrigeration is defined as the science of maintaining the temperature of a particular space lower than its surrounding space. Refrigeration and air conditioning involves various processes such as compression, expansion, cooling, heating, humidification, de-humidification, air purification, air distribution etc. In all these processes, there is an exchange of mass, momentum and energy. All these exchanges are subject to certain fundamental laws. Hence to understand and analyses the refrigeration and air conditioning systems, a basic knowledge of the laws of thermodynamics, fluid mechanics and heat transfer is essential.
Mechanical Engineering 130.2 (2008): 6 - 7. Academic Search Complete. Web. The Web. The Web.
where p is the density of the fluid (in runner’s case: air); v is the velocity of the runner; A is the cross-sectional area perpendicular to the runner’s velocity; and D is the dimensionless quantity called the drag coefficient.
Computers are also used for numerical analysis of turbulent flows in fluids. Often, a point-by-point substiitution into the Navier-Stokes Equations (below) will be used.
This involves relating the current supplied to the motor, motor shaft rotational speed, motor efficiency, and the power factor as a function of the load of the motor, similar to the figure on page 21 of the Lab Manual.
I will also be looking at more complex concepts and ideas such as Reynolds's number, the effect of temperature on viscosity and liquid density, which we have not met in last year's course. The areas I will be looking into are as follows: 1) The effect of the Pipe Diameter on flow rate. - the effect of Pipe Diameter on liquid flow (turbulent/laminar) 2)
Saravanamutto, H. I. H., Rogers, G. F. C., Cohen, H., & Straznicky, P. V. (2009). Gas turbine theory (6th ed.). London, UK: Prentice Hall.
Next Dalton’s law of partial pressure is used. The mixture of gas in the graduated cylinder was filled with two things: water vapor and air. Using the Dalton’s law, it can be concluded that the total pressure is equal to the pressure of air and the pressure of water vapor added together. This is an endothermic reaction which means that it absorbs heat, and when a reaction gains heat, it is repres...