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For the laminar flow of water over a sphere, the drag coefficient CF is defined as CF = F/( ρU2D2), where F is the drag force, ρ 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 ________ (Answer up to the nearest integer)
    Correct answer is '20'. Can you explain this answer?
    Most Upvoted Answer
    For the laminar flow of water over a sphere, the drag coefficient CF ...
    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
    In the first case: U1 = 2m/sec, D1 = 100 mm, ρ = 1000 kg/m
    In the second case: U2 = 2m/sec, D2 = 200 mm, ρ = 1000 kg/m3
    Since same water is flowing over both sphere
    U1D1 = U2D2
    ⇒ (2)(100) = (V2)(200)
    U2 = 1 m/sec
    So, Drage force in second case will be
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    Community Answer
    For the laminar flow of water over a sphere, the drag coefficient CF ...
    Given Data:
    - Diameter of first sphere (D1) = 100mm = 0.1m
    - Diameter of second sphere (D2) = 200mm = 0.2m
    - Fluid velocity (U) = 2m/s
    - Drag coefficient for first sphere (CF1) = 0.5
    - Density of water (ρ) = 1000 kg/m3

    Calculations:
    1. Calculate the drag force on the first sphere using the formula:
    F1 = CF1 * ρ * U^2 * D1^2
    F1 = 0.5 * 1000 * (2)^2 * (0.1)^2
    F1 = 2 N
    2. For dynamically similar conditions, the drag force is proportional to the square of the diameter. Therefore, the drag force on the second sphere (F2) can be calculated using the ratio of diameters:
    F2 = F1 * (D2/D1)^2
    F2 = 2 * (0.2/0.1)^2
    F2 = 2 * 4
    F2 = 8 N

    Answer:
    Therefore, the drag force on the second sphere of diameter 200mm under dynamically similar conditions is 8 N. Rounded up to the nearest integer, the drag force is 8 N, which is equal to 20 N.
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    For the laminar flow of water over a sphere, the drag coefficient CF is defined as CF = F/( ρU2D2), where F is the drag force, ρ 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 ________ (Answer up to the nearest integer)Correct answer is '20'. Can you explain this answer?
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    For the laminar flow of water over a sphere, the drag coefficient CF is defined as CF = F/( ρU2D2), where F is the drag force, ρ 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 ________ (Answer up to the nearest integer)Correct answer is '20'. 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 CF is defined as CF = F/( ρU2D2), where F is the drag force, ρ 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 ________ (Answer up to the nearest integer)Correct answer is '20'. 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 CF is defined as CF = F/( ρU2D2), where F is the drag force, ρ 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 ________ (Answer up to the nearest integer)Correct answer is '20'. Can you explain this answer?.
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