Q2/ By using the power series method make a dimensional analysis for the following variables: The frietional torque of a disc T-f(disk diameter D, rotating speed N, viscosity of fluid and its density p).
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A: Option D is the correct answer
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A: Solution: SInce number of variables is more than three, Buckingham π-theorem is more suitable for…
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A: The complete derivation is attached as an image.
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Q: Q2/ By using the power series method make a dimensional analysis for he following variables: The…
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Q: When a liquid in a beaker is stirred, whirlpool will form and there will be an elevation difference…
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Q: The thrust force of propeller (P) depends upon the flow velocity V, angular velocity o, diameter D,…
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A: Solution:
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Q: External Problem 2: Dimensional analysis and similarity The viscous torque T produced on a disc…
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Q: The spin rate of a tennis ball determines the aerodynamic forces acting on it. In turn, the spin…
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- Q2/ By using the power series method make a dimensional analysis for the following variables: The frictional torque of a disc T = f (disk diameter D, rotating speed N, viscosity of fluid µ, and its density p).1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance through the water V, acceleration due to gravity g, the angular speed of the propeller w, the water pressure 2, and the water viscosity . You want to find a set of dimensionless variables on which the thrust coefficient depends. In other words CT = Fr pV2D² = fen (T₁, T₂, ...Tk) What is k? Explain. Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V.b) When a liquid in a beaker is stirred, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (o) of the whirlpool, fluid density (p), gravitational acceleration (g), and radius (R) of the container. Take o, p and R as the repeating variables.
- 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 =1Q2/ A car wheel is supposed to be travelling at a speed of 80 mile per hour in the air. A scaled model (1:4) is tested in water instead of air and is supposed to have dynamic similarity. a) Determine the model speed in water b) then find the force ratio of the model to prototype if you know that: (pair = 1.22 kg/m³, µair = 1.78 x 10- 5 N.s/m?, Pwater 998 kg/m², µwater = 0.001 N.s/m²).When a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.
- Under a laminar flow, the liquid flows through small holes. It has a triangular cross-section, width b and length L, where the volumetric flow rate Q of the flow is a function of viscosity. ,pressure reduction per unit length p/L and width b 1) Use the PI theory to write the relationship as a dimensionless variable. 2) if the width b is doubled by viscosity And the pressure drop per unit length p/L is the same. I want to know how the flow rate Q will change.The spin rate of a tennis ball determines the aerodynamic forces acting on it. In turn, the spin rate is a§ectedby the aerodynamic torque. If the torque depends on áight speed V , density , viscosity , ball diameter D,angular velocity !, and the fuzz height, hf , Önd the important dimensionless variables for this case. Use V ,, and D as your scaling (repeating) variables.Acording to Darcy law, P is a pressure, V is a velocity, D is a diameter, g is acceleration gravity, f is dimensionless coefficient. Is the equation dimensionaly consistent?
- Some children are playing with soap bubbles, and you become curious as to the relationship between soap bubble radius and the pressure inside the soap bubble . You reason that the pressure inside the soap bubble must be greater than atmospheric pressure, and that the shell of the soap bubble is under tension, much like the skin of a balloon. You also know that the property surface tension must be important in this problem. Not knowing any other physics, you decide to approach the problem using dimensional analysis. Establish a relationship between pressure difference ΔP = Pinside − Poutside, soap bubble radius R, and the surface tension ?s of the soap film.The development of a flow situation depends on the velocity V, the density, 3 linear dimensions (L1, L2, L3), pressure drop, gravity, viscosity, surface tension, and bulk modulus of elasticity. In an analysis using the Buckingham Pi-Theorem, how many dimensionless variables can you generate? O a. 6 Pls O b. 5 Pls O c. 7 Pls Od. a PlsPide Use Buckingham's PI Theorem to determine non-dimensional parameters in the phenomenon shown on the right (surface tension of a soap bubble). The variables involved are: R AP - pressure difference between the inside and outside R- radius of the bubble Pide Soap film surface tension (Gravity is not relevant since the soap bubble is neutrally buoyant in air)