The thrust force, F generated by a propeller is found to depend on the following parameters: diameter D, forward velocity u, density p, viscosity u and rotational speed N. Determine the dimensionless parameters to correlate the phenomenon.
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- When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indicate how experimental data for this problem could be correlated. Neglect compressibility effects and the influence of surface roughness.The thrust force, F generated by a propeller is found to depend on the followingparameters: diameter D, forward velocity u, density ρ, viscosity µ and rotationalspeed N. Determine the dimensionless parameters to correlate the phenomenonThe thrust F of a propeller is generally thought to be afunction of its diameter D and angular velocity V , the forwardspeed V , and the density ρ and viscosity μ of the fl uid.Rewrite this relationship as a dimensionless function.
- The pressure coefficient is defined by the ratio between the static pressure difference and the dynamic pressure (pictured): Where P is the static pressure [Pa], P∞ is the reference static pressure [Pa], ρ is the density [kg/m3], and V is the velocity [m/s]. Using the primary dimensions and their units, show that the pressure coefficient is dimensionless.Books on porous media and atomization claim that the viscosityμ and surface tension Y of a fl uid can be combinedwith a characteristic velocity U to form an important dimensionlessparameter. ( a ) Verify that this is so. ( b ) Evaluatethis parameter for water at 20°C and a velocity of3.5 cm/s. Note: You get extra credit if you know the nameof this parameter.When a capillary tube of small diameter D is inserted into a container of liquid, the liquid rises to height h inside the tube (Fig.). h is a function of liquid density ? , tube diameter D, gravitational constant g, contact angle ?, and the surface tension ?s of the liquid. (a) Generate a dimensionless relationship for h as a function of the given parameters. (b) Compare your result to the exact analytical equation for h. Are your dimensional analysis results consistent with the exact equation? Discuss.
- The thrust force of propeller (P) depends upon the flow velocity V, angular velocity o, diameter D, dynamic viscosity , density p. the speed of sound in the medium C. (1) Derive the relationship between the above variables and the thrust force by using Buckingham's IT-theorem. (2) Explain the physical meaning of the obtained dimensionless groups. إجابتThe time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.Please solve this problem, Thank you very much! Figure is attached 1. liquids in rotating cylinders rotates as a rigid body and considered at rest. The elevation difference h between the center of the liquid surface and the rim of the liquid surface is a function of angular velocity ?, fluid density ?, gravitational acceleration ?, and radius ?. Use the method of repeating variables to find a dimensionless relationship between the parameters. Show all the steps.
- The water resistance (drag) R on the submarine Nautilus is a function of its length L, velocity v of the ship, viscosity μ, and density ρ of the water in which it moves. Determine dimensionless groups that could be used to organize test data.The quantities viscosity µ, velocity V, and surface tension Y may be combined into a dimensionless group. Find the combination which is proportional to µ. This group has a customary name, which begins with C. Can you guess its name?If an object is light, it may be supported on the surface of a fluid. The weight of the object W, supportable by the fluid, depends on the perimeter S of the object, fluid density r, surface tension s, and gravitational acceleration constant g. Determine the dimensionless groups to describe this problem.