For a fluid undergoing steady rotational flow at low Reynolds number with angular velocity w in a lindrical polar co-ordinate system (r, 0, z), we find ə or (r³ da) : ər (a) Find an expression for a (include two constants of integration) and use it to identify two types of steady circular motion. = 0. = (b) Find the magnitude of the vorticity in terms of w for each of the two cases. You may wish to use the formula for curl in cylindrical polar co-ordinates when there is no variation in the z direction, 1 (a(rue) ər VAU = ² дир ae 2.
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- Need help with number one. I have to Derive the expression for the force in the hydraulic cylinder AB as a function of theta.2.80 The fluid mechanics of the human arterial system is of vital importance to our health and safety. The specific gravity and viscosity of blood are about 1.06 and 3.3 centipoise (cp), respectively. The mean flow speed in the aorta (30 mm i.d.) of a large human is about 0.15 m/sec. Calculate the flow Reynolds number using these properties. Would you expect this flow to be laminar or turbulent?Four objects: A, B, C and D, with different weights, are placed on a rigid horizontal surface. Table 1 shows the pressure exerted by each object on the horizontal surface. Write the letter of the object that indicates the correct pressure. (You must show the calculations.) The results of all problems must be expressed in SI units, unless the problem tells you indicate in other units.
- Please hand writing answerLet v(x, y, z) = (-2z, 0, z) represent a velocity field (with units of meters per second) of a fluid with constant density 4 kg/m³. Let S be the surface of the paraboloid z = a? + y? outward. Find the mass flow rate of the fluid across S. Do not include the unit kg/sec/m2 in the answer. 4 with z < 0 such that S is orientedA rectangular solid made of aluminum has a density p= 2.70 g/cm³. The dimensions of the solid are shown below. The solid is placed on top of a truncated cone whose circular ends have the dimensions shown. The bottom of the rectangular solid down on the top surface of the cone. Find the pressure (in N/m²)between those two surfaces. (Ignore air pressure.) (1 kg = 1000 g, 1 m 100 cm) presses 10.0 cm 8.00 cm 15.0 cm r= 2.00 cm R = 6.00 cm
- The flow that passes through an artery per unit time is given by the following equation V = 3r4, where r is the radius of the artery. If we assume an initial radius of 0.17 centimeters for the artery and considering that there is an increase in the radius of 0.05 centimeters. Use differentials to estimate the approximate change in flux V.Question 1 a) Consider the forces acting on an infinitesimal fluid element located at radius r inside a star, where the star is in hydrostatic equilibrium. Show that the buoyancy force acting on the fluid element may be written as Pe dv dt = -(Pe - p)g where Pe is the density inside the fluid element, p is the density of the gas in the surrounding gas at radius r, v is the velocity of the fluid element and g is local acceleration due to gravity. For full marks you should explain each step of your derivation. b) With the aid of a diagram, explain the condition required for convection to occur by considering the small displacement of a fluid element from its original equilibrium location within a star.Calculate the gauge pressure (in Pa first, then convert) due to whole blood in an IV system such as the one shown in picture below if h = 2.03 m. b) Noting that there is an open tube, so that atmospheric pressure is exerted on the whole blood in the bottle, calculate the total pressure (absolute) exerted at the needle by the blood. Report both answers in mm of Hg.(1 atm= 14.7psi = 1.013x105 Pa= 760 mmHg; Absolute)(Density of whole blood = 1060 kg/m3)
- c) A rectangular flume is given with different roughnesses on the walls and bottom (see sketch) and a bottom gradientl=3 %0. Determine theManning-Strickler coefficient kst wthe walls according to Horton-Einstein for a flowQ=37.5m3/s and associated flow depth of=2m: (5 points) = ? st,w kstw = ? 'st,w k. = 30 m/3/s Horton-Einstein: st,s -2/3 "st,i Kst B = 8 m h = 2 mGg