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What is the formula for the total drag on a smooth sphere according to G.G. Stokes up to Reynolds number?
What is the formula for the total drag on a smooth sphere according to G.G. Stokes up to Reynolds number?
- $FD = 4 \pi \mu DU$
- $FD = 3 \pi \mu DU$ (correct)
- $FD = 2 \pi \mu DU$
- $FD = 6 \pi \mu DU$
In terms of total drag on a smooth sphere, what percentage does the skin friction drag contribute?
In terms of total drag on a smooth sphere, what percentage does the skin friction drag contribute?
- 50%
- 25%
- 33.3% (correct)
- 75%
What percentage of the total drag on a smooth sphere is attributed to pressure drag?
What percentage of the total drag on a smooth sphere is attributed to pressure drag?
- 75%
- 25%
- 33.3%
- 50% (correct)
When the Reynolds number for a sphere is between 0.2 and 5, what is the drag coefficient expressed as?
When the Reynolds number for a sphere is between 0.2 and 5, what is the drag coefficient expressed as?
What is the value of the drag coefficient for a sphere when the Reynolds number exceeds 105?
What is the value of the drag coefficient for a sphere when the Reynolds number exceeds 105?
Which law or equation determines the value of the drag coefficient for a sphere when the Reynolds number is less than 0.2?
Which law or equation determines the value of the drag coefficient for a sphere when the Reynolds number is less than 0.2?
What happens to the drag force on a cylinder when the Reynolds number is less than 1?
What happens to the drag force on a cylinder when the Reynolds number is less than 1?
At what Reynolds number value does the drag coefficient (CD) for a cylinder reach a minimum value of 0.95?
At what Reynolds number value does the drag coefficient (CD) for a cylinder reach a minimum value of 0.95?
What happens to the drag coefficient for a cylinder when the Reynolds number is 3 × 10^4?
What happens to the drag coefficient for a cylinder when the Reynolds number is 3 × 10^4?
What type of drag force is experienced when a flat plate is placed parallel to the direction of flow?
What type of drag force is experienced when a flat plate is placed parallel to the direction of flow?
At what Reynolds number does the drag coefficient for a cylinder become 0.3?
At what Reynolds number does the drag coefficient for a cylinder become 0.3?
What happens to the drag coefficient for spheres as the Reynolds number increases beyond $3 \times 10^6$?
What happens to the drag coefficient for spheres as the Reynolds number increases beyond $3 \times 10^6$?
What happens to the pressure distribution around a cylinder due to circulation?
What happens to the pressure distribution around a cylinder due to circulation?
In the Magnus effect, how is the lift force produced when a cylinder is rotated in a uniform flow field?
In the Magnus effect, how is the lift force produced when a cylinder is rotated in a uniform flow field?
What is the impact of wind flowing over a kite at 30 km/h on its drag coefficient?
What is the impact of wind flowing over a kite at 30 km/h on its drag coefficient?
How does the angle of a kite relative to the horizontal affect its lift force?
How does the angle of a kite relative to the horizontal affect its lift force?
What is the relationship between the weight of an object and its drag force according to Stoke's law?
What is the relationship between the weight of an object and its drag force according to Stoke's law?
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Study Notes
Total Drag on a Smooth Sphere
- Total drag formula as per G.G. Stokes is relevant for spheres at low Reynolds numbers.
- Skin friction drag contributes to approximately 50% of the total drag on a smooth sphere.
- Pressure drag accounts for the remaining 50% of the total drag on a smooth sphere.
Reynolds Number and Drag Coefficient
- For Reynolds numbers between 0.2 and 5, the drag coefficient (CD) for a sphere is expressed as a function of Reynolds number.
- When the Reynolds number exceeds 10^5, the drag coefficient for a sphere reaches a relatively constant value around 0.47.
- Stokes' law governs the drag coefficient for spheres when the Reynolds number is less than 0.2, where the flow is viscous and laminar.
Drag on a Cylinder
- The drag force on a cylinder is significantly affected and reduced when the Reynolds number is less than 1 due to the dominance of viscous effects.
- The drag coefficient for a cylinder reaches a minimum value of 0.95 at a Reynolds number around 3 × 10^4.
- As the Reynolds number increases to 3 × 10^4, the drag coefficient for a cylinder remains stable before increasing again with higher Reynolds numbers.
Flat Plate and Drag Forces
- A flat plate positioned parallel to the flow direction experiences viscous drag, primarily influenced by skin friction.
Influence of Reynolds Number on Drag Coefficient
- The drag coefficient for a cylinder drops to 0.3 when the Reynolds number is around 100.
- As the Reynolds number exceeds 3 × 10^6 for spheres, the drag coefficient typically experiences a decrease due to the transition toward turbulent flow.
Pressure Distribution and Lift Forces
- Circulation around a cylinder alters pressure distribution, which can create additional lift forces in certain conditions.
- The Magnus effect produces a lift force on a rotating cylinder within a uniform flow field due to differential pressure created by the rotation.
Kites and Drag Coefficient
- A kite flying in wind at 30 km/h will have its drag coefficient influenced by speed, shape, and airflow conditions.
- The angle of a kite in relation to the horizontal significantly affects its lift force; an optimal angle increases lift while adjusting drag.
Relationship Between Weight and Drag Force
- According to Stoke's law, there is a direct relationship between the weight of an object and its drag force; the drag force increases with weight in low-Reynolds-number conditions.
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