What is a fully developed laminar and turbulent flow?
Fully developed flows refer to spatial in variance of the flow in study along the direction of flow, ie. no change in properties along the direction of flow. Hydro dynamically, this implies to the first derivative of velocity along the flow direction to be zero. This is achieved by the pressure gradients which drive the flow ( accelerate the flow) being equally balanced by the shear forces ( fictional force), that retard the flow. This is true in general for any flow whether laminar or turbulent.The main difference between laminar and turbulent flows lies in the complexity of flow patterns, which are far more complicated in turbulence due to seemingly random distribution of velocities in time, accompanied by large number of vortices of various sizes present all the time. Hence, when the flow is laminar, we have pressure forces being balanced by viscous forces, which are functions of mean velocity gradients and related through viscosity. For most fluids having low viscosity like air, these are given by Newton's law. For steady pipe flows, solving the momentum equation ( Navier strokes equation) gives a parabolic velocity profile across the radius.When the flow is turbulent, the effective shear force is not related to only mean velocity gradients but dominated by a much larger term known as the Reynolds stress, which in simple terms is related to square of the turbulent velocity fluctuations. Thus, when we deal with fully developed turbulent flows, the time averaged momentum equation has an additional term which plays the same role as an enhanced viscosity. This results in the velocity profile to be different from laminar flows.Many answers have listed that the gradients for fully developed turbulent flows are steeper at the walls, followed by flattening or plug flow like profile away from the walls or boundaries. This is a result of the enhanced viscosity. Higher viscosity results in more smoothening out of velocity, thus having a " flat" profile away from the walls.
What is the Reynolds numbers for laminar and turblent flows?
The Reynolds number is the ratio of inertial forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent.It can be interpreted that when the viscous forces are dominant (slow flow, low Re) they are sufficient enough to keep all the fluid particles in line, then the flow is laminar. Even very low Re indicates viscous creeping motion, where inertia effects are negligible. When the inertial forces dominate over the viscous forces (when the fluid is flowing faster and Re is larger) then the flow is turbulent.[math]R=\frac{\rho V D}{\mu}[/math]where:V is the flow velocity,D is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter etc.)ρ fluid density (kg/m³)μ dynamic viscosity (Pa.s),ν kinematic viscosity (m²/s); ν = μ / ρ.Laminar flow:Re < 2000‘low’ velocityFluid particles move in straight linesLayers of water flow over one another at different speeds with virtually no mixing between layers.The flow velocity profile for laminar flow in circular pipes is parabolic in shape, with a maximum flow in the center of the pipe and a minimum flow at the pipe walls.The average flow velocity is approximately one half of the maximum velocity.Turbulent Flow:Re > 4000‘high’ velocityThe flow is characterized by the irregular movement of particles of the fluid.Average motion is in the direction of the flowThe flow velocity profile for turbulent flow is fairly flat across the center section of a pipe and drops rapidly extremely close to the walls.The average flow velocity is approximately equal to the velocity at the center of the pipe.
Volumetric flow rate, parallel plates?
Looks as though the plates have a width of 1 m, working back from the anwer you have given. Was that information supplied to you? A=1.79/22.4 m^3 A=w x h h=0.08 w= (1.79/22.4)/0.08=0.999 m It is a rectangular duct, right? Not a circular pipe i.e. area is not pi.r^2 ! Laminar velocity profile means it is a parabola, but you have been given the mean, which seems sufficient to determine the correct answer; provided you know the plates are 1 m wide.
Can I find someone who can show me the velocity distribution of a non-Newtonian fluid? Is it still parabolic?
As James Stiles pointed out, it is not going to be parabolic. It will depend on the type of the fluid. For pseudoplastic fluids, the profile is going to be flat in the middle. However, for dilatant fluids, the velocity distribution is going to look like a bullet (i.e. it will get pointy).In the simulation below, a non-Newtonian fluid is simulated on a sudden expansion tunnel.In the picture below, the upper half of the domain is shown. As you can see, the velocity profile (across the red line of the first image) is more flat near the middle on the first image (pseudoplastic), while it is more parabolic in the middle (Newtonian), and gets more “pointy” in the third image (dilatant).You can see the simulation here: Non-Newtonain flow through a sudden expansion and you can modify the simulation parameters yourself to check the effects.
What is the best way to determine the pipe flow rate from pressure and diameter?
I can’t tell if your question is one of practical concern, or one of theoretical interest.If theoretical, use the Hagen–Poiseuille equation. This equation relates mean velocity, pressure drop and length of pipe.In fully developed laminar flow, the velocity profile across a section of the pipe is a parabolic curve. The average velocity is half the maximum velocity at the center line of the pipe.10 diameters can be taken as the length required to develop laminar flow.This may be fairly useless information in practical use where elbows and Tees in the pipe add further pressure drop and result in turbulence flow.
I need answer to this important fluid flow question, how to calculate laminar flow in pipes.?
Interesting question. The laminar velocity profile is theoretically parabolic, let's say U = constant*[1 - (r/R)^2]. (The "constant" is of course "U-max") So what we're after is [integral of U dr from r=0 to R/2] divided by [integral of U dr from r=0 to R]. We don't need the "constant," it will cancel when we consider the ratio. Integral of [1 - (r/R)^2] dr = r - (r^3)/(3R^2) so the desired ratio is [R/2 - R/24] / [R - R/3] = (11/24)/(2/3) = 11/16. I've gone over this several times without finding my error (if any); perhaps you or another responder will come up with a different answer, but I don't see my answer among your choices.
What do you mean by flow is fully developed?
Let's consider the flow of fluid in the pipe from tankAs the fluid enters the pipe by virtue of no slip condition bondary layer will happen and the fluid will acquire the velocity of pipe adjacent to pipeAs we move further in the radial direction the velocity in the center of the pipe will increase and the velocity profile will tend to acquire the shape of parabola from the flat profile at the entrance point.After we get the parabola shape of velocity profile…even if we move further along the length of pipe velocity profile remains same that is du/dx=0 after that cross sectionFrom the entrance point up to the perfect parabolic shape it is known as entrance length or entrance region. It is the distance travelled by the flow before it becomes fully developed. beyond this region we will get a fully developed flow.Also at the starting cross section of fully developed flow two boundary layers of pipe meetFor laminar flow to know the length of entrance region use the formula L/d=0.06*Reynolds noFor turbulent flow L/d=4.4*Reynolds no to the power 1/6Where L=entrance length d=dia of pipe
Bernoulli's energy equation is not applicable in boundary layer due to viscous effects, then why we apply it in case of pipe flows?
The development of boundary layer in a pipe flow can be explained from the diagram above. As you see, there are two regions in which the flow can be divided. The first portion is the entry length where viscous effects dominate. The thickness of the boundary layer increases till it reaches the centerline and a fully developed velocity profile is said to be formed.Assuming that the flow is Newtonian, the wall shear stress at any instant of time is given byTo answer your question: During the initial stages of the flow, the thickness of the boundary layer is small and wall shear stress is the highest due to rapidly changing gradients. Hence in this region, viscous effects dominate the flow. However, as we reach the parabolic velocity profile, the largest gradients are only at the wall resulting in higher shear stress. Due to the parabolic profile, the shear stresses decrease as you get closer to the centerline and eventually become zero.It’s a good approximation to consider the flow as inviscid near the centerline and effects of shear stresses near the walls. We can also define an average velocity at a cross section. It’s fairly obvious from the diagram that the velocity profile will reach the average velocity close to the wall, reducing the “effective boundary layer thickness” and helping us apply the potential flow theory.Remember that these are merely approximations which have give practical results over many years and hence are accepted. There will always be some shear stress existing everywhere. It entirely depends on what length scale you will be looking at in the problem.As we reduce the diameter of the pipe to a very small value, viscous effects will dominate throughout the cross section and we will get a type of the flow called as Hele Shaw flow.Boundary layershttps://www.uio.no/studier/emner...Hele-Shaw flow - WikipediaBoundary layers