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- A one-fortieth-scale model of a ship’s propeller is tested in atow tank at 1200 r/min and exhibits a power output of 1.4ft . lbf/s. According to Froude scaling laws, what should therevolutions per minute and horsepower output of the prototypepropeller be under dynamically similar conditions?water (ρ = 1000 kg / m ^ 3, v = 1.0 * 10 ^ -6 m ^ 2 / s, μ = 1.0 * 10 ^ -3 kg / ms) flows from a 50 cmm diameter pipe at 2 m / s . A model of this system will use air (ρ = 1.2 kg / m ^ 3, v = 1.5 * 10 ^ -5 m ^ 2 / s μ = 1.8 * 10 ^ -5 kg / ms) as fluid . Air velocity will be 30 m / s. Find the required pipe diameter to achieve dynamic similarity between model and prototype.A 1:30 model of a ship is made. The real ship has a hull length of 130 m and travels at 7.9 m/s. Find the fraude number. If there is a dynamic similarity and froude # criterion applies, what should the velocity of the mdoel ship be?
- The variation of fluid pressure with height is described by the differential equation: dp/dz = - density *g Here, p is specific density and g is the local acceleration of gravity. For an ideal gas, p = M PIRT, where M is molar mass and R is the universal gas constant. Modeling the atmosphere as an isothermal column of ideal gas at 283.15 K (lO°C), estimate the ambient pressure in Denver, where z = l(mi1e) relative to sea level. For air, take M = 29 g molP1; values of R are given in App. A.A diver 50 m deep in 8°C fresh water exhales a 1.2 cm diameter bubble which rises to the surface of the water and has a diameter of 2.2 cm when it reaches the surface of the water. Assume the air bubble rises slow enough that it is always in thermal equilibrium with the surrounding water. Include units in all your numerical responses 1. Determine the pressure of the air inside the bubblesThe vertical cross section of an irrigation canal is modeled by f (x) = 5x2 / x2+ 4 where x is measured in feet and x = 0 corresponds to the center of the canal. Use the integration capabilities of a graphing utility to approximate the fluid force against a vertical gate used to stop the flow of water when the water is 3 feet deep?
- The 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?The power P generated by a certain windmill design depends on its diameter D, the air density p, the wind velocity V, the rotation rate w and the number of blades n. a) Write this relationship in dimensionless form. A model windmill of diameter 50 cm develops 2.7 kW at sea level when V=40 m/s and when rotating at 4800 r/min. b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude? c)What is the appropriate rotation rate of the prototype?An engineer is to design a human powered submarine for a design competition. The overall length of the prototype submarine is 2.24 m and its engineer designers hope that it can travel fully submerged through water at 0.560 m/s. The water is freshwater (a lake) at 7-15°C (p=999.1 kg/m3 and u= 1.138 ×103 kg/m-st. The design team builds a one-eighth scale model to test in their university's wind tunnel. The air in the wind tunnel is at 25°C (p= 1.180 kg/m3 and u = 1.849 ×10-5 kg/m-s) and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve 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?Consider the case of a model of a hydroelectric dam for which it is required developing two dimensionless performance parameters. Take in to acount the volume of water stored Va, the diameter of the discharge pipe d, the head of available water h (net height of the dam) and the discharge flow Q. Although they are constant, you will surely have to consider the local gravity g and the density of water r. The parameters of interest are the instantaneous hydraulic power PotH and empty time td.Applying principles of dynamics, with step by step solutions pls (i give 5 stars) A usual football tryout involves a player running a 40-yard dash. If a particular player finishes the dash in 4.25 seconds while reaching his maximum speed at the first 16 yard mark with a constant acceleration and then maintains that speed for the remainder of the run, determine this person’s acceleration over the first 16 yard, his maximum speed and how long he accelerated. SET YOUR OWN VARIABLES AS YOU SEE FIT.