[1] Consider steady flow of air through the diffuser portion of a wind tunnel. Along the centerline of the diffuser, the air speed decreases from uentrance to uat as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, x=0 to x=L.
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- 4. Consider steady flow of water through an axisymmetric garden hose nozzle (see Fig). Along the center line of the nozzle, the water speed increases from uentrance to Uexit as sketched. Measurements reveal that the centerline water speed increases parabolically through the nozzle. Write an equation for centerline speed u(x), based on the parameters given here, from x=0 to x=L. Dentrance Dexit Hentrance Hexit u(x) x=LA 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?In 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.
- The less following data is measured for the dimensionless velocity u of a fluid as a function of dimensionless location and dimension- time t: t=0 t=2 t = 4 t = 6 t = 8 x=0 0 3 14 7 5 x=0.5 8 10 14 12 10 x = 1 2 7 8 9 7 x = 1.5 13 15 22 16 9 x=2 15 18 22 17 14 By hand, calculate the acceleration of the fluid, ou/et and the spatial change in acceleration of the fluid, ²u/(Ətəx) a) at z = 1 and t4 with second order accuracy; b) at z = 0 and t = 2 with second order accuracy;The slope of the height h of a surface wave moving in a shallow pool of liquid is related to the speed of the wave u and gravity g by the following equation и ди дх g əx (a) Use a length scale L and a velocity scale Vo to 'nondimensionalize' the equation (b) What is the nondimensional parameter of the flow?The Reynolds transport theorem (RTT) is discussed in Chap. 4 of your textbook. For the general case of a moving and/or deforming control volume, we write the RTT as follows: d pb dV + pbV-ñ dA dt dt dB sys where Vr is the relative velocity, i.e., the velocity of the fluid relative to the control surface. Write the primary dimensions of each additive term in the equation and verify that the equation is dimensionally homogeneous. Show all your work. (Hint: Since B can be any property of the flow-scalar, vector, or even tensor—it can have a variety of dimensions. So, just let the dimensions of B be those of B itself, {B}. Also, b is defined as B per unit mass.)
- Consider steady flow of air through the diffuser portion of a wind tunnel. Along the centerline of the diffuser, the air speed decreases from uentrance to uexit as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, from x = 0 to x = L.[Q6] (a) At this instant, find angular acceleration and angular velocity for CD using Absolute motion method. II- Relative motion method III- Show that results from both methods are identical 10 m/s a-16 m/s 300 mm 3 mm (b) Find work done in a process in which P(V-0.6)*-10 When volume is changed from 0.2 m to 1.5 mProblem 1: Streamlining From dimensional analysis, we know the drag force is FD- CopAV2/2, where Cp is a dimensionless coefficient of drag. The two space shuttles below have the same area A, the same velocity V, and are flying through the same air. Which has a smaller Co and why? (<25 words) thine e
- A Fluid Mechanics, Third Edition - Free PDF Reader E3 Thumbnails 138 FLUID KINEMATICS Fluid Mechanies Fundamenteis and Applicationu acceleration); this term can be nonzero even for steady flows. It accounts for the effect of the fluid particle moving (advecting or convecting) to a new location in the flow, where the velocity field is different. For example, nunan A Çengel | John M. Cinbala consider steady flow of water through a garden hose nozzle (Fig. 4-8). We define steady in the Eulerian frame of reference to be when properties at any point in the flow field do not change with respect to time. Since the velocity at the exit of the nozzle is larger than that at the nozzle entrance, fluid particles clearly accelerate, even though the flow is steady. The accel- eration is nonzero because of the advective acceleration terms in Eq. 4-9. FLUID MECHANICS FIGURE 4-8 Flow of water through the nozzle of a garden hose illustrates that fluid par- Note that while the flow is steady from the…A periodic Kármán vortex street is formed when an uniform stream flows over a circular cylinder (Figure Q4). By applying method of repeating variables or Buckingham Pi's Theorem, determine a dimensionless relationship for Kármán vortex shedding frequency (fx.) as a function of free-stream speed (V), fluid density (p), fluid viscosity(u), and cylinder diameter (D). Q4 V D Figure Q4A 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?