Show that Reynold number, pud/µ, is non-dimensional.
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Q: Convert the quantities 300 lb s and 52 slug/ft' to appropriate SI units. SOLUTION Using Table 1
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- Q) The velocity v (m/s) of air flowing past a flat surface is measured at several distances y(m) away from the surface. Use Newton'sviscosity law to determine the shear stress t (N/m³) at the surface (y=0). dv 'dy Assume a value of dynamic viscosity =1.8* 10- N.s/hm² y, m V, m/s 0.002 0.287 0.006 0.899 0.012 |1.915 0.018 3.048 0.024 4.299 (r-7) Use two forward đifference approximations for h=0.006. Estimate the approximate percent relative error, &. b- , (t=?) Use two forward difference approximations with a step size of 0.012 (h=0.012). Estimate the approximatepercent relative error, , e.. (r-?) ApplyRichardson extrapolation. Estimate the approximate percent relative error, & (r=?) Use unequally spaced three data and the first-derivative of a second-order d- Langrange polynomial to evaluate the derivative (y=0) and shear stress. Estimate the approximate percent relative error, Eg Compare the approximate estimates of the error ([ed ) for the formulas used.Dynamic viscosity of fluid Density of fluid If X= , then the unit of X is = O m?/kg O m/sec? O m/sec O m?/sec The container contains an oil of specific gravity 0.64 with the pressure measured at the bottom of the container is 150 Pa. Find the pressure head in m of oil. The pressure head of oil in m = If the density of fluid is not a variable in a fluid flow, it is known as O Incompressible O Unsteady flow O Uniform flow O CompressibleQuestion 2: The pressure drop, AP, in a horizontal pipe depends on the pipe diameter, d, pipe length, L, pipe roughness, &, average velocity, V, density of the fluid, p, and absolute viscosity of the fluid, u. Express the variables in non-dimensional form using Buckhingham-Pi theorem (25 Points)
- The resistance R, to the motion of a completely submerged body depends upon the length of the body L, velocity of flow V, mass density of fluid p and kinematic viscosity of fluid v. By dimensional analysis prove that R = pr* L') VL' = pV?1Q1: Apply appropriate solution method using math principles to prove that "the pressure at a point in a fluid has the same magnitude in all directions". Support your answer with sketch. Answer: Px Pz = Pn P are the mean pressures at the three surfaces in the x- and z-directions. Q2: Formulate the issue and identify key variables to prove that [AP = P2 - P, = pg Az = y, Az], where y, and p are the specific weight and density of the fluid, respectively. Az is the vertical distance. Support your answer with sketch. Q3: From fluid mechanics science perspective, define the center of gravity and the center of pressure. Q4: Identify the hydrostatic force acting on the top surface of a submerged rectangular plate by applying principles of engineering for the following cases: 1 tilted plate, (2 vertical plate, and 3 horizontal plate. Support your answer with sketch. Q5: By applying principles of fluid mechanics science, define the "rigid-body" and identify its features. Q6: Formulate the issue…7. Aflat thin plate is dragged at a constant velocity of 4 m/s on the top of a 5 mm deep liquid layer of viscosity 20 centipoise. If the area of the plate is 1 m² find the drag force. Assume variation of velocity in the liquid to be linear. [Ans. 16 N]
- A catheter-sensor system for invasive pressure measurements has a catheter with a length of 1 m and a diameter of 2.5 mm. The catheter is filled with water at 20 C, with viscosity = 0.001 Pa.s and density = 103 kg/m3. The diaphragm elasticity Ed equals 0.5x1015 N/m5. a. Draw the simplified electrical model of the pressure measurement set-up that includes the catheter and the diaphragm and determine the transfer function of the pressure measurement system. b. Compute the natural frequency and damping ratio of this system. c. The current system has a damping ratio that is far from optimal. Suppose you are pinching the catheter for a small length lx so that the catheter diameter reduces to 0.2mm. Assuming the pinch to affect the resistance only, determine the length lx such that an optimal damping ratio = 0.7 is obtained. d. Suppose that the assumption of purely resistive effects of the pinch cannot be made. Discuss (without calculations) the consequences on the derivation of lx.Q2:- If the velocity of flow v, dynamic viscosity a, bulk modulus of elasticity K and diameter of pipe D, using dimensional analysis, determine the general form of relationship between these variables.Q5: The compart ments (8) 4 C) in figure below are closed & filled with air. When the gauges (A) 4 (D) read as indicated, what should be the value of Cx) for gaugeCE)? (Mereury in each U-tube gauge) 2.07 bar 254 Air Air E x
- Question 2: The pressure drop, AP, in a horizontal pipe depends on the pipe diameter, d, pipe length, L, pipe roughness, ɛ, average velocity, V, density of the fluid, p, and absolute viscosity of the fluid, u. Express the variables in non-dimensional form using Buckhingham-Pi theorem1) At any time, approximately 20 volcanoes are actively erupting on the Earth, and 50–70 volcanoes erupt each year. Over the past 100 years, an average of 850 people have died each year from volcano eruptions. As scientists and engineers study the mechanics of lava flow, accurately predicting the flow rate (velocity) of the lava is critical to saving lives after an eruption. Jeffrey's equation captures the relationship between flow rate and viscosity as: Flow V = Pgt sin(@) 28 сm 10 where p is the density of the lava, g is gravity, t is the flow thickness, a is the slope, and u is the lava viscosity. Typical values are given as follows for the flow rate: u= 4x103 kg/(m.s) ±1% p= 2.5 g/cm³ ±1% t= 28 cm +0.5 cm a= 10° +1 ° g= 9.81 m/s? Determine the likely maximum possible error in the calculated value of the flow rate.58.27 cm Determine the shear stress acting on the fluid element for a velocity profile of 5*y+1 and viscosity of 0.25 kg/(m*sec) by using Newton's law of viscosity? 5 Pa 0.25 Pa none 2.25 Pa 1.25 Pa 1 bar pressure difference is equal to .. water manometer height. Take water specific gravity as 1 O O O