Did I calculate the boundary layer thickness correctly?

In summary, the boundary layer thickness is the layer of fluid near a solid surface that affects flow characteristics. It can be calculated using various methods and is influenced by factors such as fluid velocity, viscosity, surface roughness, and shape. The accuracy of calculations depends on the method and assumptions used, and common mistakes include using incorrect equations or assumptions and neglecting important factors. Careful review and validation with experimental data can help minimize errors.
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PhyIsOhSoHard
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Homework Statement


A flat plate moves in water (20°C) in the direction of the plate at a speed of 1 m/s. What is the boundary layer thickness 0.1 meter downstream of the plate?

Homework Equations


Reynolds number:
##Re_x=\frac{xU_∞}{\nu}##

Boundary layer thickness for laminar flow:
##\frac{\delta}{x}=\frac{5.0}{\sqrt{Re_x}}##

The Attempt at a Solution


Reynolds number is:
##Re_x=\frac{xU_∞}{\nu}=\frac{1m/s\cdot 0.1m}{9\cdot 10^{-7}}=1.1\cdot10^5##

Boundary layer thickness:
##\frac{\delta}{x}=\frac{5.0}{\sqrt{Re_x}}=\frac{5.0}{\sqrt{1.1\cdot10^5}}=0.015##

##\frac{\delta}{x}=0.015⇔##

##\delta=0.015\cdot 0.1m=0.0015m=1.5mm##
 
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1. What is the boundary layer thickness and why is it important?

The boundary layer thickness refers to the layer of fluid near a solid surface where the flow of the fluid is affected by the presence of the surface. It is important because it can affect the overall flow characteristics, such as drag, heat transfer, and pressure distribution.

2. How is the boundary layer thickness calculated?

The boundary layer thickness can be calculated using various methods, such as the momentum integral method, energy integral method, or numerical simulations. The specific method used will depend on the specific flow conditions and properties of the fluid.

3. What are the factors that affect the boundary layer thickness?

The boundary layer thickness is influenced by several factors, including the velocity of the fluid, viscosity of the fluid, surface roughness, and the shape and size of the solid surface. These factors can also affect the type of boundary layer, whether it is laminar or turbulent.

4. How accurate are boundary layer thickness calculations?

The accuracy of boundary layer thickness calculations depends on the method used and the assumptions made. In general, calculations using more complex methods or experimental data tend to be more accurate than simplified calculations. However, it is important to validate the results with experimental data whenever possible.

5. What are some common mistakes when calculating boundary layer thickness?

Some common mistakes when calculating boundary layer thickness include using incorrect equations or assumptions, neglecting important factors such as surface roughness or density changes, and not considering the effects of transition from laminar to turbulent flow. It is important to carefully review all assumptions and double-check calculations to minimize these errors.

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