What is nikuradse equation?

The Nikuradse-Prandtl-von Karman (NPK) equation is the most widely used expression to determine friction factors for fluid flow in smooth pipes [1–3]. It implicitly relates the friction factor (expressed here as f; sometimes called λ) to the Reynolds number, Re. It is shown in Equation (1).

What is nikuradse roughness?

Dimensionless Nikuradse roughness (ks/D, where D is the sediment diameter) is usually given 1–2.5 on the immobile plan bed or at low shear stress. But it behaves differently on the mobile plan bed at high shear stress with much sediment picked up to movement when the Shields parameter (Θ) is larger than 0.8–1.0.

What is a turbulent flow used for?

Common examples of turbulent flow are blood flow in arteries, oil transport in pipelines, lava flow, atmosphere and ocean currents, the flow through pumps and turbines, and the flow in boat wakes and around aircraft-wing tips.

What is turbulent flow Reynolds?

At Reynolds numbers between about 2000 and 4000, the flow is unstable due to the onset of turbulence. These flows are sometimes referred to as transitional flows. Turbulent flow. If the Reynolds number is greater than 3500, the flow is turbulent. Most fluid systems in nuclear facilities operate with turbulent flow.

What is Epsilon fluid?

K-epsilon (k-ε) turbulence model is the most common model used in computational fluid dynamics (CFD) to simulate mean flow characteristics for turbulent flow conditions. The second transported variable is the rate of dissipation of turbulent kinetic energy (ε).

How is Reynolds number calculated?

The Reynolds number (Re) of a flowing fluid is calculated by multiplying the fluid velocity by the internal pipe diameter (to obtain the inertia force of the fluid) and then dividing the result by the kinematic viscosity (viscous force per unit length).

How does friction factor vary with the Reynolds number and the surface roughness for laminar flow?

For laminar flow (Re < 2100), the friction factor was independent of the surface roughness and it varied linearly with the inverse of Reynolds number.

What is equivalent sand grain roughness?

The equivalent sand grain roughness model was proposed by Schlichting [1] and is an empirical model in which rough surfaces with various shapes of roughness elements are compared to data from Nikuradse [2] regarding flow in pipe with varying size of sieved sand glued to the surface.

What is an advantage of turbulent flow?

A turbulent flow can be either an advantage or disadvantage. A turbulent flow increases the amount of air resistance and noise; however, a turbulent flow also accelerates heat conduction and thermal mixing. Therefore, understanding, handling, and controlling turbulent flows can be crucial for successful product design.

How do you know if a flow is turbulent or laminar?

For practical purposes, if the Reynolds number is less than 2000, the flow is laminar. If it is greater than 3500, the flow is turbulent. Flows with Reynolds numbers between 2000 and 3500 are sometimes referred to as transitional flows.

What can we learn from Nikuradse’s experiment?

I recommend the work of Joann Nikuradse, who in the 1930s measured the hydraulic effects of uniform sand grain roughness on the flow in cylindrical pipes. Nikuradse, a Georgian-born German engineer and physicist, conducted his famous experiment in 1933, which was published in 1937 [25]; remarkably, his results have survived the test of time.

What is niknikuradse’s criterion of turbulent flow separation?

Nikuradse took δ* instead of θ. The numerical value of Γ ≈ –0·06 is a criterion of turbulent flow separation if Γ increases rapidly approaching the position of turbulent flow separation. Furthermore, Buri [ 10] found that by integrating the steady-state momentum equation

What is the formula for turbulent flow separation?

Γ a = ue(due / dx)θϱ τw and ζ(Γ a) = τw ϱu2e (ueθ v)1 / 4. This form of Γ is similar to the parameter which Nikuradse used. Nikuradse took δ* instead of θ. The numerical value of Γ ≈ –0·06 is a criterion of turbulent flow separation if Γ increases rapidly approaching the position of turbulent flow separation.

What is the Blasius equation of Karman-Nikuradse?

Equation of Blasius Equation of Karman–Nikuradse By combining Eq. (7.4) with Eq. (7.7), the relationship h = cv1.75 (here c is a constant) arises, giving the relationship for turbulent flow in Fig. 7.4. Dr.Boyun Guo, Dr.Ali Ghalambor, in Natural Gas Engineering Handbook (Second Edition), 2005