An underwater device which is 2m long is to be moved at 4 m/sec. If a geometrically similar model 40 cm long is tested in a variable pressure wind tunnel at a speed of 60 m/sec with the following information, Parater = 998kg/m* Pair at Standard atmospheric pressure = 1.18kg/m3 1.80 x 10-5 Pa-s at local atmospheric pressure and Hwater = 1 x 10-3 Pa-s then the pressure of the air in the model used times local atmospheric pressure Hair %3D is
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- 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.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.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?
- Pide 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)Answer all the questions 1) Using dimensional equations, convert: 700 m* /(day. kg) to cem* /(min. g). 2) Convert 210 X 10 kJ/min to hp 3) Calculate the weight in lbr of a 30.0-lbm object. 4) Calculate the mass in kg of an object that weighs 25 Newton. 5) The density of a fluid is given by the empirical equation: p = 70.5 exp(8.27 x 10-7P) where p is density (Ib/ft) and Pis pressure (lb,/in.?). (a) What are the units of 70.5 and 8.27 x 10-7? (b) Calculate the density in g/cm for a pressure of 9.00 x 10 N/m?. 6) The vapor pressures of 1-chlorotetradecane at several temperatures are tabulated here. T(C) 98.5 131.8 148.2 166.2 199.8 215.5 p* (mm Hg) 1 5 10 20 100 60 Use two different method to estimate the value of P' at T = 190 °C (7) The specific gravity of gasoline is approximately 0.70. a- Determine the mass (kg) of 50.0 liters of gasoline. b- The mass flow rate of gasoline exiting a refinery tank is 1150 kg/min. Estimate the volumetric flowrate in liters/s.A small low-speed wind tunnel is designed to calibrate hot wires (anemometer wires) (Figure 2). The air temperature is 19 OC. The test section of the wind tunnel is 30 cm in diameter and 30 cm in height. The flow through the test section must be as uniform as possible. The speed range of the wind tunnel varies from 1 M/s to 8 M/S, and the design will be optimized with an airspeed of V= 4.0 M / s in the test section. For a flow state at a speed of 4.0 m/S, which is almost uniform at the entrance to the test section, how fast does the air velocity on the tunnel axis accelerate to the end of the test section?Note: kinematic viscosity of air at 19 C ν=1. 507x10-5 m2 / s
- using pure water at 20°C. The velocity of the prototype in seawater (p = A 1/18 scale model of the submarine is to be tested in the water tunnel 1015 kg/m³, v = 1.4x106 m²/s) is 3 m/s. Determine: a) the speed of the water in the water tunnel for dynamic similarity D) the ratio of the drag force on the model to the drag force on the prototypeP1.20 A baseball, with m = 145 g, is thrown directly upward from the initial position z = 0 and Vo = 45 m/s. The air drag on the ball is CV², as in Prob. 1.19, where C~ 0.0013 N: s*/m". Set up a differential equation for the ball motion, and solve for the instantaneous velocity V(t) and position z(1). Find the maximum height zmax reached by the ball, and compare your results with the classical case of zero air drag.A2) In order to solve the dimensional analysis problem involving shallow water waves as in Figure 2, Buckingham Pi Theorem has been used. h Figure 2 Through the observation that has been done, the wave speed © of waves on the surface of a liquid is a function of the depth (h), gravitational acceleration (g), fluid density (p), and fluid viscosity (µ). By using this Buckingham Pi Theorem: a) Analyze the above problem and show that the Froude Number (Fr) and Reynolds Number (Re) are the relevant dimensionless parameters involve in this problem. b) Manipulate your Pi (1) products to get the parameter into the following form: pch := f(Re) where Re = Fr = c) If one additional primary variable parameter involve in this proolem such as, temperature (T). Discuss on the Pi (m) products that can be produce and explain why this dimensional analysis is very important in the experimental work.
- A student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 95 (m), and its student designers hope that it can travel fully submerged through water at 0.440 m/s. The water is freshwater (a lake) at T = 15°C. The design team builds a one-fifth scale model to test in their university’s wind tunnel. A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag. The air in the wind tunnel is at 25°C and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achievesimilarity?Suppose we know little about the strength of materials butare told that the bending stress σ in a beam is proportionalto the beam half-thickness y and also depends on thebending moment M and the beam area moment of inertiaI . We also learn that, for the particular case M = 2900in ∙ lbf, y = 1.5 in, and I = 0.4 in4 , the predicted stressis 75 MPa. Using this information and dimensional reasoningonly, find, to three significant figures, the onlypossible dimensionally homogeneous formula σ=y f ( M , I ).MLT By dimensional analysis, obtain an expression for the drag force (F) on a partially submerged body moving with a relative velocity (u) in a fluid; the other variables being the linear dimension (L), surface roughness (e), fluid density (p), and gravitational acceleration (g).