Experimental studies have shown that the rate of the decay of kinetic energy for homogeneous isotropic turbulence (HIT) is k~t¯", with 1.1
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- The erythrocyte sedimentation rate (heaviness) test of a blood sample is often used as a diagnosis of immune disorders and some other diseases. Assuming that the red blood cells are about a sphere with a diameter of (approximately 5 um) and a density (g/ml 1.125), and the density and viscosity of the plasma in which the red blood cells are settled (Pa.s), (1025 kg/m3 10-3 x 1.5) On arrangement and acceleration m/s2 9.81 Calculate the erythrocyte sedimentation rate (settlement rate). 9:40 73% * "l Asiacell 90 x 10-6 m/s 1 0.9 x 10-6 m/min 90 x 10-6 m/minUse the Stokes-Einstein equation to estimate the diffusivity (cm^2/s) for a molecule with a solute radius 6.5 nm, at 29 degrees C, in a fluid with viscosity of 0.82 cP). Enter your answer in decimal form without unitsUse the Stokes-Einstein equation to estimate the diffusivity (cm^2/s) for a molecule with a solute radius 2.6 nm, at 44 degrees C,in a fluid with viscosity of 1.01 cP). Enter your answer in decimal form without units
- A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Assuming kinetic viscosity, v = 30 x 10-6 m²/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is (up to three decimal)?5) Consider a vessel of diatomic nitrogen gas at room temperature. (a) What is the most likely speed of a molecule? (b) How fast does a molecule have to be traveling to be in the top 5%? (Hint: For (a), use DESMOS to make a graph of the Maxwell-Boltzmann velocity distribution and locate the maximum on the graph. For (b), integrate the Maxwell-Boltzmann distribution numerically. See planetcalc.com/5494)An ESP with a total plate area of 5000 m2 treats 8000 m3/min of air containing particulate matter of essentially one diameter. If the electrostatic force per unit mass cm a particle is 2000 times the force of gravity and the slip-corrected characteristic time, z,for this partidedn-air system is 5.1(10)-6 sec, calculate the efficiency of the ESP,
- In the experiment of high Reynolds number, an airfoil of width, W= 30 cm, and chord length, C = 24 cm is subjected to airflow at 1 atm and 5 °C as shown in Figure 2.1. The airfoil can be approximated as a flat plate. The total drag force acting on the airfoil is 40.2 N. The pressure drag acting on the airfoil is measured to be 39.9 N by using pressure sensors throughout the surface. Given, the drag coefficient of the airfoil is Cp = 0.04, the density and kinematic viscosity of air at 1 atm and 5 °C is 1.269 kg/m³ and 1.382 x 10$ m²/s, respectively. i. Determine the friction drag coefficient of the airfoil. ii. Verify that the boundary layer flow at the trailing edge is turbulent. V C Figure 2.1 The airflow on a streamlined bodyWhich choice is not a scaling parameter used to nondimensionalize the equations of motion? (a) Characteristic length, L (b) Characteristic speed, V (c) Characteristic viscosity, ? (d ) Characteristic frequency, f (e) Gravitational acceleration, gWhat are the physical and quantitative evidence of turbulence in fluid flow?
- Using dimensional analysis obtain an expression for nusselt number in terms of Reynolds number and prandtl number1.What is the difference between laminar and turbulent flow, and how does this affect fluid mechanics in mechanical engineering?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.