Calculate Max Velocity V to Achieve Laminar Flow in Water at Re=200

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In summary, to determine the maximum velocity needed for a laminar, linear flow distribution with a height of 3 mm, the Reynolds number must be calculated using the equation Re = average velocity x height/kinematic viscosity. The limiting Reynolds number for this type of flow is 200. After solving for the Reynolds number and obtaining a value of 600, it is clear that the maximum velocity needed for laminar, linear flow has been exceeded. Further calculations or adjustments may be needed to achieve the desired flow distribution.
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Homework Statement



If the fluid water with kinematic viscosity v=1 x 10^-6 m^2/s and density of 1000 kg/m^3, determine the Max velocity V that an upper plate could be moved to produce a laminar, linear, flow distribution when the height is 3 mm. The limiting Reynolds number for a laminar linear velocity profile is Re = 200.(Recall that the Reynolds number is formed using average flow velocity)

Homework Equations



Re = average velocity x height/kinematic viscosity
Shear Stress(T)= dynamic viscosity x Velocity of plate/height
Average velocity = area under profile/flow depth

The Attempt at a Solution



I have been able to solve for the Reynolds number, but I am not sure what to do after.
 
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I got a Reynolds number of 600, which is above the limiting Reynolds number. How do I determine the max velocity?
 

1. What is the equation for calculating maximum velocity for laminar flow in water at Re=200?

The equation for calculating maximum velocity (V) to achieve laminar flow in water at a Reynolds number (Re) of 200 is: V = (Re * μ) / (ρ * L), where μ is the dynamic viscosity of water, ρ is the density of water, and L is the characteristic length of the system.

2. How do you determine the dynamic viscosity of water?

The dynamic viscosity of water can be determined using various methods, such as viscometry or rheometry. However, for practical purposes, it can also be obtained from published tables or online databases based on the temperature and pressure of the water.

3. Can laminar flow occur at Reynolds number greater than 200?

No, laminar flow is only possible at low Reynolds numbers, typically below 200. At higher Reynolds numbers, the flow becomes turbulent and chaotic, with eddies and vortices forming, leading to increased drag and energy loss.

4. Why is laminar flow desirable in certain applications?

Laminar flow is desirable in certain applications, such as in pipes or channels, because it offers lower resistance and energy loss compared to turbulent flow. This results in more efficient flow and reduced pressure drop, making it useful in industries such as water treatment, oil and gas, and chemical processing.

5. What factors can affect the maximum velocity for laminar flow in water?

The maximum velocity for laminar flow in water can be affected by factors such as the viscosity and density of water, the geometry and surface roughness of the system, and the flow conditions (e.g. temperature, pressure, and flow rate). Changes in these parameters can alter the Reynolds number and thereby impact the maximum velocity required for laminar flow.

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