a) Derive an expression for a relation between pressure and area changes in one- dimensional, steady and isentropic flow dp kM2 dA - M² ) A b) Derive an expression for a relation of pressure change across the normal shock wave (1+ kM}) (1 + kMŽ) P2 %3D P1 c) Prove mathematically that shock wave cannot occur in subsonic flow
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- Please anybody answer this ASAP,i need the answer in 40 min Air flows through a normal shock wave, upstream conditions are V₁= 650 m To1= 550 k and po₁= 750 kPa. Calculate the downstream determine conditions: *)Ma2, *)T2, *)p2 and *)02.Mott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?One of the conditions in using the Bernoulli equation is the requirement of inviscid flow. However there is no fluid with zero viscosity in the world except some peculiar fluid at very low temperature. Bernoulli equation or inviscid flow theory is still a very important branch of fluid dynamics for the following reasons: (i) (ii) There is wide region of flow where the velocity gradient is zero and so the viscous effect does not manifest itself, such as in external flow past an un- stalled aerofoil. The conservation of useful energy allows the conversion of kinetic and potential energy to pressure and hence pressure force acting normal to the control volume or system boundary even though the tangential friction stress is absent. It allows the estimation of losses in internal pipe flow. (A) (i) and (ii) (B) (i) and (iii) (ii) and (iii) All of the above (C) (D)
- Carbon dioxide has a specifi c heat ratio of 1.30 and a gasconstant of 189 J/(kg ∙ ° C). If its temperature rises from20 to 45 ° C, what is its internal energy rise?( a ) 12.6 kJ/kg, ( b ) 15.8 kJ/kg, ( c ) 17.6 kJ/kg, ( d ) 20.5 kJ/kg,( e ) 25.1 kJ/kgIn the field of air pollution control, one often needs to sample the quality of a moving airstream. In such measurements a sampling probe is aligned with the flow as sketched in Fig. A suction pump draws air through the probe at volume flow rate V· as sketched. For accurate sampling, the air speed through the probe should be the same as that of the airstream (isokinetic sampling). However, if the applied suction is too large, as sketched in Fig, the air speed through the probe is greater than that of the airstream (super iso kinetic sampling). For simplicity consider a two-dimensional case in which the sampling probe height is h = 4.58 mm and its width is W = 39.5 mm. The values of the stream function corresponding to the lower and upper dividing streamlines are ?l = 0.093 m2/s and ?u = 0.150 m2/s, respectively. Calculate the volume flow rate through the probe (in units of m3/s) and the average speed of the air sucked through the probe.A viscous fluid of density 1200 kg/m3 and viscosity 0.9 Pa.s is confined in a spacing of 0,01 m between two parallel and horizontal plates of length 0,6 m and width 0,6 m. The upper plate is pulled with a uniform and steady speed of 0,7 m/s in its own plane. The lower plate is stationary. Viscous fluid flow is laminar steady and incompressible. a) What is the magnitude of mass flow rate in spacing (in kg/s)? b) What is the magnitude of maximum shearing stress in the flow field (in Pa)? c) What is the frictional force over the lower plate surface (in N )? d) What is the frictional power lost in pulling the upper plate (in W)?
- (b) A Formula 1 team tests their car in a wind tunnel at a scale of 50%, at a speed of Vwinarunnet = 50 m/s. The measured downforce at this speed is Foownforce.WT = 3000 N and the model reference area is Aref wT = 0.5 m?. 1. Find the downforce magnitude on the full-scale race car at the same Reynolds number. Assume constant air density p = 1.2 kg/m. II. It is said that F1 cars could travel upside down, as shown below. At what speed should the full-scale car travel to achieve this, if its mass is m = 740 kg? The acceleration of gravity is g = 9.81 m/s?. Downforce Weight-5 2 Air stream k = 0.02439 W/m.K, v 1.426 x10 m /s, Pr = 0.7336) flows over a flat surface [L= 4.5 m, w = 2.5 m] with velocity of 97 km/hr, flow is parallel to L, What is the amount of heat transfer "kW" when the temperature difference is 84 °C?Q.5 A plate 1 mm distance from a fixed plate, is moving at 500 mm/s by a force induces a 2 shear stress of 0.3 kg(f)/m. The kinematic viscosity of the fluid (mass density 1000 kg/ 3. m) flowing between two plates (in Stokes) is
- In fluid mechanics, which of the following are true: (a) Fluid mechanics is the branch of science concerned with stationary fluids (b) Fluids like water posses only potential energy (c) The field of fluid mechanics is infinite and endless (d) It is a branch of physics which concerns the study of liquids and the ways in which they interact with forces (e) It is a sience concerned with the response of fluids to forces exerted upon them, (f) the fluid which is in state of rest is called as static fluid and its study is called as statics.Q2) A) Apply the principle of dimensional analysis to the problem of a screw propeller and assume that the diameter d, speed of advance V, density of flow p, viscocity coefficient of fluid u, and N (rpm). Show that the thrust T is d N T = p d? v² ø (av) bdV V B) What is the difference between the gross head and net head, with the help of a sketch?In the following section, at least 2 to up to 5 answers may be correct. 1) For a fluid, the assumption (simplifying notion) of incompressibility has important consequences: Pascal’s principle: a change of pressure in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. pressure changes are transmitted immediately from one place to another. the speed of sound then is infinite (just within this approximation). pressure becomes unpredictable. none of the above. 2) Archimedes’ principle can be summarized as: an immersed object is buoyed up by a force equal to the weight of the fluid it displaces. a bathtub is fun, and may lead to important physical discoveries regarding the volume of an object and how much water it displaces, and the weight of that amount of water. boats swim because of the work done by sailors. submarines are always doomed. fish swim because they are less heavy than water 3) A…