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
- In two dimensions along the converging nozzle, stable, considering incompressible flow. The velocity on the horizontal centerline (x-axis) is given as V=V1(1+x/L)i Derive an equation for the acceleration of a particle moving along the centerline using (a) Euler's approximation and (b) Lagrangian approximation. Discuss the acceleration for the particle being at the beginning and end of the channel.arrow_forwardWater is flowing at 0.075 cu.m./sec through a glazed porcelain pipe 400m long and 200mm diameter. The pipe roughness is 0.0015mm. Properties of water: Density: 1,000 g/cu.m., viscosity = 0.001 N-m/sec. What is the velocity of water in the pipe? What is the Reynold's number? Steady State flow exists in pipe that undergoes a gradual expansion from a diameter of 6in. Assuming constant density and the inlet flow velocity is 22.4 ft/sec. What is the size of the exit pipe if the exist flow velocity is 12.6 ft/sec?arrow_forward1. Obtain Bernoulli’s equation for compressible flow considering adiabatic process. 2, Define vortex flow. Derive an expression of stream function and velocity potential function for vortex flow. 3. What is Venturi meter? Derive an expression for discharge through venturi meter. 4. What is Venturi meter? Derive an expression for discharge through venturi meter.arrow_forward
- Given the steady, incompressible velocity distribution V =3 x i + Cy j + 0 k , where C is a constant, if conservation ofmass is satisfi ed, the value of C should be( a ) 3, ( b ) 3/2, ( c ) 0, ( d ) - 3/2, ( e ) - 3arrow_forwardVelocity components in the flow of an ideal fluid in a horizontal plane; Given as u = 16 y - 12 x , v = 12 y - 9 x a) Is the current continuous?(YES OR NO) b) Can the potential function be defined?(YES OR NO) c) Find the unit width flow passing between the origin and the point A(2,4). (y(0,0)=0) d) Calculate the pressure difference between the origin and the point B(3;3).arrow_forwardFigure 1) shows a tank of 20∘C water with a nozzle h = 27 cm below the surface. Bernoulli's equation applies to the flow between points 1 and 2 on the streamline, but not to the flow between points 2 and 3.What is the volume flow rate through the nozzle in L/min ? Assume that the water level in the tank is held constant.arrow_forward
- Consider two sinusoidal sine waves traveling along a string, modeled as y1 (x, t) = 0.3 m sin (4 m−1 x − 3 s−1 (t)) and y2 (x, t) = 0.3 m sin (4 m−1 x + 3 s−1 (t)). What is the wave function of the resulting wave? [Hint: Use the trig identity sin(u ± v) = sin u cos v ± cos u sin varrow_forward6 For incompressible flow, density remains the same Select one: True Falsearrow_forwardPlease indicate the given, assumption and illustration. A source with strength 0.25 m2/s and a vortex with strength 1 m2/s (counter-clockwise) are located at the origin. After working out the equations for the stream function and velocity potential components, determine the following velocity components at a point P(1, 0.5): A) The Radial Velocity component in meters/second. B) The Tangential Velocity Component in meters/second.arrow_forward
- A velocity profile for water is given as a function of x, y and z. How can we determine if the profile is a physically possible flow field? A) If the sum of the derivatives of each component with respect to their flow direction = 0. B) If the flow is irrotational. C) If the vorticity equals 0. D) If we can determine a velocity potential.arrow_forwardWater at 20◦C flows along the streamlines shown in Figure3.11. The (gauge) pressure, velocity, and elevation at Point1 are 15.0 kPa, 1.0 m/s, and 5.02 m, respectively, and thevelocity and elevation at Point 2 are 0.5 m/s and 5.21 m,respectively. Estimate the pressure at Point 2. The given answer was P2 = 13.5 kPa. Show detailed solution pls thank you.arrow_forwardAssume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. Consider a venturi with a small hole drilled in the side of the throat. Thishole is connected via a tube to a closed reservoir. The purpose of theventuri is to create a vacuum in the reservoir when the venturi is placed inan airstream. (The vacuum is defined as the pressure difference below theoutside ambient pressure.) The venturi has a throat-to-inlet area ratio of0.85. Calculate the maximum vacuum obtainable in the reservoir when theventuri is placed in an airstream of 90 m/s at standard sea level conditions.arrow_forward
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