Fluid particle at some later time t OA' Fluid particle at time t = 0
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Converging duct flow is modeled by the steady, two-dimensional velocity field V-›= (u, ? ) = (U0 + bx) i-›− byj-› where U0 is the horizontal speed at x = 0. A fluid particle (A) is located at x = xA and y = yA at time t = 0. At some later time t, the fluid particle has moved downstream with the flow to some new location x = xA′, y = yA′, as shown in the figure. Generate an analytical expression for the y-location of the fluid particle at arbitrary time t in terms of its initial y-location yA and constant b. In other words, develop an expression for yA
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- A- Given that the volumetric flow rate for a fluid within a circular cross-section tube can be represented by Q= πΡΑ ΔΡ 8μL where r is the tube radius, µ is the fluid viscosity, P is the pressure drop across the tube, and L is the tube length, calculate the pressure drop across a tube of length 1 m and diameter of 23 mm. The fluid is blood (μ = 0.0035 N.s/m²) and has a volumetric flow rate of 4.5 L/min. Assuming the same conditions, what would the required pressure drop be for water (μ = 0.001 N.s/m²) and chocolate syrup (μ = 150 N.s/m²).Water is flowing through the pipe from left to right. Write an equation for the pressure difference between points A and B. If at point A the velocity of the water is 3 m/s when the diameter of the pipe is 10 cm and the pressure of the water is 1.5x 105 Pa at point A, what is the pressure at point B?The terminal speed of a spherical partide falling in a liquid is given by where R is the radius of the sphere, e, is its density, p, is the density of the fluid, and n is the coefficient of viscosity. Using this equation, find the viscosity (in mPa · s) of motor oil in which a steel ball of radius 0.9 mm falls with a terminal speed of 4.83 cm/s. The densities of the ball and the oil are 7.86 and 0.88 g/mL, respectively. mPa - s
- A fluid flows between two points inside a tube with pressure difference (P₂ - P₁) of 1.00 x 104 [Pa] and height difference (y2 - y₁) of 1.00 [m]. The exit speed v₁ of the fluid is 10.0 [m/s] and the inner diameter of entrance pipe d2 is twice the diameter of exit pipe d₁. What is the density of the fluid?A balloon filled with helium gas has an average density of ρb = 0.31 kg/m3. The density of the air is about ρa = 1.23 kg/m3. The volume of the balloon is Vb = 0.075 m3. The balloon is floating upward with acceleration a. Express the acceleration a in terms of F, ρb and Vb.A cube of side length and density pc is immersed in a fluid of density pf. Let h be the height of the cube that is immersed in the fluid. Then, a slight downward push is applied on the cube, making it oscillate up and down the fluid. е Pc h Pfl b. Is the period for small oscillations explicitly dependent on the densities of the fluid and the cube? O Yes O No
- A spherical shell has an outside radius of 2.40 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.52 g/cm3. The space inside the shell is filled with a liquid having a density of 1.27 g/cm3. (a) Find the mass m of the sphere, including its contents, as a function of a. m = g (b) For what value of a does m have its maximum possible value? a = cm (c) What is this maximum mass? m = g (d) Explain whether the value from part (c) agrees with the result of a direct calculation of the mass of a solid sphere of uniform density made of the same material as the shell. (e) Would the answer to part (a) change if the inner wall were not concentric with the outer wall? Yes NoA balloon filled with helium gas has an average density of ρb = 0.39 kg/m3. The density of the air is ρa = 1.23 kg/m3. The volume of the balloon is Vb = 0.045 m3. The balloon floats upward with acceleration a. a.) Express the acceleration of the balloon a in terms of the variables given in the problem statement, assuming upwards is the positive direction. b.) Calculate the numerical value of a in m/s2.The lower section of a constricted pipe has a diameter of 8 cm. The upper section of the pipe, located 0.1 m above the lower section, has a diameter of 3 cm. The pressure at the lower section is 2.1 ×× 104 Pa, while the pressure in the upper section is 1 ×× 104 Pa. Assuming water moves through the pipe in a steady flow, calculate the speed (in m s-1) of the flow in the lower section. The density of water is 1000 kg m-3.
- A balloon filled with helium gas has an average density of ρb = 0.31 kg/m3. The density of the air is about ρa = 1.23 kg/m3. The volume of the balloon is Vb = 0.075 m3. The balloon is floating upward with acceleration a. Calculate the numerical value of F in N.A submersible vehicle is in ocean at a depth of 26.2 m. What is the absolute pressure (in Pa) at this depth? The density of the water in the ocean is 1.00 X 103 kg/m³, and the air above is at a pressure of 101.3 kPa. Submit your answer in exponential form.For modeling and calculation purposes, architects treat air as an incompressible fluid. As an architect's intern, you are doing the specs on a dorm air conditioning system that is designed to replace the air in each room every twenty-three minutes. If the rooms each have a volume of 200 m3and they are supplied by ducts with a square cross section, determine the following. (a) the length of each side of a duct if the air speed in the duct is to be 3.6 m/s. m (b) the length of each side of a duct if the air speed at the duct is to be a value twice this speed.m