Problem 6-1: The Reynolds number is an engineering parameter that relates to the volume flow rate of a fluid 4Q πνd where vis through a tube of diameter d as Red the fluid kinematic viscosity. Determine the Reynolds number and its uncertainty by general analysis given m³ d = 50.4 ±0.1 mm, Q = 0.213 +0.005 S

Please solve correctly, Show unit conversion (I don't know why there is conversion factor 1488 in the numerator)

Reynolds number for pipe flow may be expressed as Re = (4 m/ Trd) / µ Where m = mass flow, kg/s d= pipe diameter, m p = viscosity, k/m s In a certain system, the flow rate is 5.448 kg/min +0.5 %, through a 0.5" (inch) diameter (±0.005"). The viscosity is 1.92x 10-5 kg/m s, ±1 %. Calculate the value of the Reynolds Number and its uncertainty. Determine the main contribution to uncertainity.

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.

On a single plot, show curves that show the relationship between the pressure generated by thepump as a function of flow rate of water at 20 °C through the three branches of the piping systemshown below (delta P on the y axis and flow rate on the x axis; therange of the pressure should be 0 to ~1 MPa).  Pipe inner diameter: 0.03 mPipe material: copperTypical mass flow rate of interest: 0.5 kg/sIgnore minor losses of tee's at points A and B and any features of branch 3Consider minor losses of two 90° elbows in branch 2

On a single plot, plot three curves that show the relationship between the pressure generated by thepump as a function of flow rate of water at 20 °C through the three branches of the piping systemshown below. Delta P on y axis and flow rate on the x axis. The pressure range is 0 to 1 MPa. (Branches 1 and 3 are in the same plane; branch 2 is located 5 m above the other two branches. Pipe inner diameter: 0.0254 mPipe material: copperTypical mass flow rate of interest: 0.5 kg/sIgnore minor losses of tee's at points A and B and any features of branch 3Consider minor losses of two 90° elbows in branch 2

Consider the setup shown below, with a valve to adjust the flow of a fluid to an orifice meter equipped with a differential manometer across it, in series with a rotameter that has been previously calibrated for liquid acetone (density= 0.791 g/cm3), the fluid of interest.  The rotameter calibration expression was found to be V=1.56R, where the volumetric flow rate is in mL/s and the rotameter reading is unitless.  The manometer fluid has a specific gravity of 1.210.  a) For one valve setting resulting in a rotameter reading of 82.0 as liquid acetone flows through the system, the height difference of the manometer fluid is 22.0 mm.  The volumetric flow rate for this condition in mL/s with 3 sig. fig's is b) For one valve setting resulting in a rotameter reading of 80.0 as liquid acetone flows through the system, the height difference of the manometer fluid is 22.3 mm.  The pressure drop for this condition in Pascals (Pa) with 3 sig. fig's is

n = Xe()r -------Equation 1 where X = 1.7419 and (E/R) = -0.018 are constants for a given fluid. You are required to carry out appropriate calculations on the effect of changes in temperature given in table A by using equation 1 for Ethanol on the viscosity of a fluid. Table A NO Temperature viscocity n T°C cP 10 3 20 30 5 40 6. 50 7 60 8 70 In addition to this, calculate other constraints such as the variety of shear stress (T) and force due to fluid viscosity, when the two layers of different compressible Newtonian fluids are contained between two flat plates separated by a distance of 0.05m and fluid moving with the velocity of 2m/s in the horizontal direction. Assume the shear area between the fluid layers is 0.5m². To do this you required to explain, with examples, the effects of temperature and shear forces on Newtonian and non-Newtonian fluid. Also, explain the operation and constraints of different viscometers that quantify viscosity in fluids. 2.

Fluid

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.