List and describe the three necessary conditions for complete similarity between a model and a prototype.
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Q: 1. Explain the three necessary conditions which must be met in order to achieve complete similarity…
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A: For solution refer below images.
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List and describe the three necessary conditions for complete similarity between a model and a prototype.
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- Give Justification for performing a geometrically scaled model rather than the full-scale prototype in the technique of dimensional analysis and similarity.Ship whose full length is 100 m is to travel at 10 m/sec. For dynamical similarity, with what velocity should a 1:25 model of the ship be towed?Although we usually think of a model as being smaller than the prototype, describe at least three situations in which it is better for the model to be larger than the prototype.
- Here, a 1:10 scale prototype of a propeller on a ship is to be tested in a water channel. What would the rotating speed of the model be if the rotational speed of the p propeller is 2000 rpm, and if: (a) the Froude number governs the model-prototype similarity(b) Reynolds number governs the similarityA one-fourth scale model of a car is to be tested in a wind tunnel. The conditions of the actual car are V = 45 km/h and T = 0°C and the air temperature in the wind tunnel is 20°C. In order to achieve similarity between the model and the prototype, the wind tunnel is run at 180 km/h. The properties of air at 1 atm and 0°C: ? = 1.292 kg/m3, ? = 1.338 × 10−5 m2/s. The properties of air at 1 atm and 20°C: ? = 1.204 kg/m3, ? = 1.516 × 10−5 m2/s. If the average drag force on the model is measured to be 70 N, the drag force on the prototype is (a) 66.5 N (b) 70 N (c) 75.1 N (d ) 80.6 N (e) 90 NThe resistance of a sea-going ship is due to wave-making and viscous drag, and it may be expressed in functional form as where FD is the drag force, V is the ship speed, L is its length, B is its width, ρ and µ are the sea water density and viscosity, and g is the gravitational constant. (a) Find the nondimensional parameters that describe the problem. (b) If we are to test a model of the ship, what are the requirements for dynamic similarity? (c) We are going to test a 1/25th scale model of a 100 m long ship. If the maximum velocity of the full-scale ship is 10 m/s, what should the maximum speed of the model be? What should the kinematic viscosity of the model test fluid be compared to the kinematic viscosity of sea water?
- Oil (kinematic viscosity, v = 1.0 x 10-5 m³/s) flows through a pipe of 0.5 m diameter with a velocity of 10 m/s. Water (kinematic viscosity, V = 0.89 x 10-6 m²/s) is flowing through a model pipe of diameter 20 mm. For satisfying the dynamic similarity, the velocity of water (in m/s) is %3D WSpeed is usually a function of density, gravitational acceleration, diameter, height difference, viscosity, and length. Using the repetitive variables method and taking density, gravitational acceleration, and diameter as repetitive variables, find the required dimensionless parameters. V = f(p, g, D, Az, u, L)1:25 scale model of a submarine is tested at 180 ft/s in a wind tunnel using sea-level standard air. What is the prototype speed in seawater at 20°C for dynamic similarity? If the model drag is 1.6lb, what is the prototype drag?
- This problem is (16.23) from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND? b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/m² and the dynamic viscosity is 0.2 N.s/m². For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s/m². kg.m IN =1The efficiency of a fan, n, can be expressed as a function of fan's diameter, D, its angular velocity, w, the discharge, Q, and fluid's kinematic viscosity, v. Derive an expression for efficiency, n, using Buckingham Pi theorem. If a model is being constructed with a model to prototype ratio of 1:20, and assuming that the angular velocity of the prototype is 5 rad/s, what would be the angular velocity of the model? Also, if the discharge is 0.5 m³/s for the prototype, what will be the discharge for the model? (Ambient fluid for both model and prototype is air)