A one-fourth scale model of an airplane is to be tested in water. The airplane has a velocity of 700 km/h in air at −50°C. The water temperature in the test section is 10°C. In order to achieve similarity between the model and the prototype, the test is done at a water velocity of 393 km/h.              The properties of air at 1 atm and −50°C: ? = 1.582 kg/m3, ? = 1.474 × 10−5 kg/m·s.                                                                                 The properties of water at 1 atm and 10°C: ? = 999.7 kg/m3, ? = 1.307 × 10−3 kg/m·s.                                                                                                       If the average drag force on the model is measured to be 13,800 N, the drag force on the prototype is (a) 590 N (b) 862 N (c) 1109 N (d ) 4655 N (e) 3450 N

A cube of side (a) and mass (M) is initially sitting fully submerged at the bottom of a container filled with a liquid of kinematic viscosity v and density p. The container has a square cross-section of side (a+a/5) and the cube is sitting right at the middle of the container base. (a) A force (F) starts pulling the cube up at a constant velocity (U). Develop an expression for the force in terms of (U, M. a. g, p and v). You may assume that the velocity in the gap between the cube's sides and the container walls is linear. The expression for (F) is to be valid as long as the cube remains submerged. (b) After the cube reaches the water surface, it continues to be pulled up by the same force. Develop a differential equation for the variation with time of the fraction of the cube that is submerged in water.

A block of mass 4.0 kg moves horizontally on a film of crude oil at 30°C. The contact area of the undersurface is 0.06 m². If initially the block has a speed of 3.0 m/s, find the speed after 1 s. Dynamic viscosity of crude oil at 30° is 1.65 x 10-3 Pa.s. The oil film thickness below block is 0.3mm.

The wind flutter on the wing of a newly proposed jet fighter is given by the following 1st order differential equation: dy/dx = 2yx   With the Boundary Condition:  y(0) = 1  (remember this means that y = 1 when x = 0)   Determine the vertical motion (y) in terms of the span (x) of the wing.   The frequency of fluctuations of the wing at mach 2 is given by the non-homogenous 2nd order differential equation: y'' + 3y' - 10y = 100x   With the boundary conditions: y(0) = 1  and  y(1) = 0  (i.e., y = 1 when x = 0  and  y = 0 when x = 1)   By solving the homogenous form of this equation, complete the analysis and determine the amplitude (y) of vibration of the wing tip at mach 2.   Critically evaluate wing flutter and fluctuation frequency amplitude determined by solving the two differential equations above.

The rate of heat loss Qloss through a window or wall is athe function of the temperature difference between insideand outside ∆ T , the window surface area A , and the Rvalue of the window, which has units of (ft 2 .h . ° F)/ Btu.( a ) Using the Buckingham Pi Theorem, find an expressionfor the rate of heat loss as a function of the other threeparameters in the problem. ( b ) If the temperaturedifference ∆ T doubles, by what factor does the rate ofheat loss increase?

A one-third scale model of an airplane is to be tested in water. The airplane has a velocity of 900 km/h in air at −50°C. The water temperature in the test section is 10°C.                                                                                                 The properties of air at 1 atm and −50°C: ? = 1.582 kg/m3, ? = 1.474 × 10−5 kg/m·s.                                                                                The properties of water at 1 atm and 10°C: ? = 999.7 kg/m3, ? = 1.307 × 10−3 kg/m·s.                                                                                                  In order to achieve similarity between the model and the prototype, the water velocity on the model should be (a) 97 km/h (b) 186 km/h (c) 263 km/h (d ) 379 km/h (e) 450 km/h

A sample of powdered zinc oxide, density 5.60g/cm 3 , is allowed to settle under the accelerationof gravity, 981 cm/sec 2 , at 25 25°C. The rate ofsettling, v, is 7.30 ×10 3 cm/sec; the density ofthe medium is 1.01 g/cm 3 , and its viscosity is 1centipoise = 0.01 poise or 0.01 g/cm sec.Calculate the Stokes diameter of the zinc oxidepowder.Problem:

Fluid mechanics deals -----_in static and dynamic conditions O Liquids and gases O Liquids only O Gases and solids O Liquids and solids

As measured by NASA’s Viking landers, the atmosphereof Mars, where g ≈ 3.71 m/s 2 , is almost entirely carbondioxide, and the surface pressure averages 700 Pa. The temperatureis cold and drops off exponentially: T ≈ T o e - Cz ,where C = 1.3E-5 m - 1 and T o = 250 K. For example,at 20,000 m altitude, T ≈ 193 K. ( a ) Find an analyticformula for the variation of pressure with altitude.( b ) Find the altitude where pressure on Mars has droppedto 1 pascal.