The Richardson number is defined as
Miguel is working on a problem that has a characteristic length scale L, a characteristic velocity V, a characteristic density difference
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Fluid Mechanics Fundamentals And Applications
- 1ODiem # The side thrust F, for a smooth spinning ball in a fluid is a function of the ball diameter D, the free-stream velocity V, the densityp, the viscosityu, and the angular velocity of spino. F= f( D, ρ, μ, V, ω) Using the Buckingham Pi theorem to express this relation in dimensionless form. Farrow_forwardA 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 / sarrow_forwardQ1: If an air stream flowing at velocity (U) pasta body of length (L) causes a drag force (F) on the body which depends only upon U, L, and fluid viscosity μ. Formulate the suitable dimensionless parameter of the air drag force.arrow_forward
- Taylor number (Ta) is used here to describe the ratio between the inertia effect and the viscous effect. By applying Buckingham Pi's Theorem, determine an equation for Ta as a function of the radius of inner cylinder (r), cylinder tangential velocity (v), fluid dynamic viscosity (u), gap distance (L) and fluid density (p). Q4arrow_forwardA simply supported beam of diameter D , length L , and modulusof elasticity E is subjected to a fluid crossflow of velocityV , density ρ , and viscosity μ . Its center deflection δ isassumed to be a function of all these variables. ( a ) Rewritethis proposed function in dimensionless form. ( b ) Suppose itis known that δ is independent of μ , inversely proportionalto E , and dependent only on ρ V 2 , not ρ and V separately.Simplify the dimensionless function accordingly. Hint:Take L , ρ , and V as r e peating variables.arrow_forwardEXAMPLE Leaking Tank. Outflow of Water Through a Hole (Torricelli's Law) This is another prototype engineering problem that leads to an ODE. It concerns the outflow of water from a cylindrical tank with a hole at the bottom. You are asked to find the height of the water in the tank at any time if the tank has diameter 2 m, the hole has diameter 1 cm, and the initial height of the water when the hole is opened is 2.25 m. When will the tank be empty? 2.20 M Water level asime Outiine walls 200 200 30t .00- 50- D 10000 30000 tebe Revelion 50000arrow_forward
- Please help me to answer these questions by today. Please try to explain it in details sothat I can understand.arrow_forward(a) Show that the Weber number is dimensionless: V √o/pL Where is the surface tension, V velocity, p density, and L is length. We = =arrow_forwardIn the orifice and Jet flow experiment, the following data were collected: Water level = 30 cm , Volume V {V} L was collected in time 32 seconds, orifice diameter = 6 mm, X1 = 50 mm , X2 = 100 mm, X3 = 150 mm, X4 = 200 mm, X5 = 250 mm Y1 = 3 mm, Y2 = 10 mm, Y3 = 22 mm, Y4 = 38 mm, Y5 = 63 mm What is the actual velocity of water jet that leaves the orifice (m/s)?arrow_forward
- fluid mechanicsarrow_forwardIn 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.arrow_forwardViscosity of fluid plays a significant role in the analyses of many fluid dynamics problems. The viscosity of water can be determined from the correlation: H = c, where µ = viscosity (N/s · m²) T = temperature (K) C, = 2.414 × 10-5 C; = 247.8 (K) Cz = 140 (K) What is the appropriate unit for c, if the preceding equation is to be homogeneous in units?arrow_forward
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