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KIRIT
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Question In flow over a flat plate, how to calculate pressure drop by knowing displacement thickness values at 2 points. Free stream velocity is known.
Calculating Pressure Drop with Displacement Thickness
- Thread starter KIRIT
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In summary, to calculate pressure drop in flow over a flat plate, you can use the Bernoulli's equation by knowing the displacement thickness values at two points and the free stream velocity.
Question In flow over a flat plate, how to calculate pressure drop by knowing displacement thickness values at 2 points. Free stream velocity is known.
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tiny-tim
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Welcome to PF!
Hi KIRIT! Welcome to PF!
Show us what you've tried, and where you're stuck, and then we'll know how to help.
Hi KIRIT! Welcome to PF!
Show us what you've tried, and where you're stuck, and then we'll know how to help.
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NatSusan
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There are a few different ways to approach this question, but one possible method would be to use the Bernoulli's equation, which relates the pressure, velocity, and height of a fluid at different points in a flow. In this case, since we know the free stream velocity and the displacement thickness values at two points, we can use the following equation:
P1 + (1/2)ρV1^2 + ρgh1 = P2 + (1/2)ρV2^2 + ρgh2
Where:
P1 and P2 are the pressures at the two points
ρ is the density of the fluid
V1 and V2 are the velocities at the two points
g is the acceleration due to gravity
h1 and h2 are the heights at the two points
Since we are interested in the pressure drop, we can rearrange this equation to solve for P1 and P2:
P1 - P2 = (1/2)ρ(V2^2 - V1^2) + ρg(h2 - h1)
From the displacement thickness values, we can determine the height difference between the two points (h2 - h1). And since we know the free stream velocity, we can calculate the velocity difference (V2^2 - V1^2). Plugging these values into the equation, we can solve for the pressure drop (P1 - P2).
Keep in mind that this is just one possible approach and there may be other methods or equations that could be used to calculate the pressure drop. It would also be important to make sure that all units are consistent and to double check any assumptions made in the calculation.
Related to Calculating Pressure Drop with Displacement Thickness
1. What is displacement thickness?
Displacement thickness is a term used in fluid mechanics to describe the decrease in effective cross-sectional area of a flow channel due to the presence of a boundary layer. It represents the distance by which the boundary layer would need to be displaced to maintain the same mass flow rate in the channel.
2. How is displacement thickness calculated?
Displacement thickness is calculated by integrating the velocity profile across the boundary layer and dividing it by the free stream velocity. This integral is then subtracted from the boundary layer thickness to obtain the displacement thickness.
3. Why is displacement thickness important in pressure drop calculations?
Displacement thickness affects the velocity and pressure distribution within the boundary layer, which in turn affects the overall pressure drop in a flow system. It is a crucial factor in accurately predicting pressure drops in various flow scenarios.
4. How does displacement thickness affect the laminar and turbulent flow regimes?
In laminar flow, the displacement thickness is typically larger than the boundary layer thickness, indicating a larger effect on the pressure drop. In turbulent flow, the displacement thickness is typically smaller than the boundary layer thickness, but it still plays a significant role in pressure drop calculations.
5. Can displacement thickness be neglected in pressure drop calculations?
No, displacement thickness should not be neglected in pressure drop calculations. It is an important factor in accurately predicting pressure drops, especially in low Reynolds number flows where the effect is more significant. Neglecting displacement thickness can lead to errors in pressure drop calculations.
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