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For the laminar flow of water over a sphere, the drag coefficient CF is defined as
CF = F /(ρU2 D2) , where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________
CF = F /(ρU2 D2) , where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________
Correct answer is between '19.9,20.1'. Can you explain this answer?
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Verified Answer
For the laminar flow of water over a sphere, the drag coefficient CFis...
Given that the condition is dynamic similarity, and in the given condition, Inertia and viscous force plays major role, hence Reynold‟s number should be same for both model and prototype.
(Re)1 = (Re)2
(Re)1 = (Re)2
In the first case:
U1 = 2m/sec, D1 = 100 mm, ρ = 1000 kg/m3
U1 = 2m/sec, D1 = 100 mm, ρ = 1000 kg/m3
In the second case: U2 = 2m/s , D2= 200mm, ρ = 1000kg/m3
Since same water is flowing over both sphere
μ1 = μ2 , ρ1 = ρ2
U1D1 = U2D2
Most Upvoted Answer
For the laminar flow of water over a sphere, the drag coefficient CFis...
Given data:
Density of water (ρ) = 1000 kg/m³
Diameter of sphere 1 (D₁) = 100 mm = 0.1 m
Fluid velocity (U₁) = 2 m/s
Drag coefficient (Cf₁) = 0.5
Formula:
Drag coefficient (Cf) = Drag force (F) / (0.5 * ρ * U² * D²)
Calculation:
Step 1: Calculate the drag force (F₁) on sphere 1:
Using the given formula, we can rearrange it to find the drag force:
F₁ = Cf₁ * 0.5 * ρ * U₁² * D₁²
F₁ = 0.5 * 1000 * (2)² * (0.1)²
F₁ = 20 N
Therefore, the drag force on sphere 1 is 20 N.
Step 2: Calculate the drag coefficient (Cf₂) for sphere 2:
We know that the flow conditions are dynamically similar for both spheres. This means that the drag coefficient for the two spheres will be the same.
Cf₁ = Cf₂
Step 3: Calculate the drag force (F₂) on sphere 2:
Using the drag coefficient equation, we can rearrange it to find the drag force on sphere 2:
F₂ = Cf₂ * 0.5 * ρ * U₂² * D₂²
We are given that the diameter of sphere 2 (D₂) is 200 mm = 0.2 m.
We need to find the fluid velocity (U₂) for sphere 2.
Since the flow conditions are dynamically similar, the ratio of velocities (U₁/U₂) is equal to the ratio of diameters (D₁/D₂).
U₁/U₂ = D₁/D₂
2/U₂ = 0.1/0.2
2/U₂ = 0.5
U₂ = 4 m/s
Now we can calculate the drag force on sphere 2:
F₂ = 0.5 * 1000 * (4)² * (0.2)²
F₂ = 80 N
Therefore, the drag force on sphere 2 is 80 N.
Conclusion:
The drag force on the sphere of diameter 200 mm under dynamically similar conditions is 80 N, which falls within the range of 19.9 N to 20.1 N as given in the correct answer.
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Community Answer
For the laminar flow of water over a sphere, the drag coefficient CFis...
At least, solve correctly then give ans , ans is 20*4=80
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For the laminar flow of water over a sphere, the drag coefficient CFis defined asCF = F /(ρU2 D2), where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________Correct answer is between '19.9,20.1'. Can you explain this answer?
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For the laminar flow of water over a sphere, the drag coefficient CFis defined asCF = F /(ρU2 D2), where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________Correct answer is between '19.9,20.1'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about For the laminar flow of water over a sphere, the drag coefficient CFis defined asCF = F /(ρU2 D2), where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________Correct answer is between '19.9,20.1'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the laminar flow of water over a sphere, the drag coefficient CFis defined asCF = F /(ρU2 D2), where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________Correct answer is between '19.9,20.1'. Can you explain this answer?.
For the laminar flow of water over a sphere, the drag coefficient CFis defined asCF = F /(ρU2 D2), where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________Correct answer is between '19.9,20.1'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about For the laminar flow of water over a sphere, the drag coefficient CFis defined asCF = F /(ρU2 D2), where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________Correct answer is between '19.9,20.1'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the laminar flow of water over a sphere, the drag coefficient CFis defined asCF = F /(ρU2 D2), where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________Correct answer is between '19.9,20.1'. Can you explain this answer?.
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