19 The Weber number is a dimensionless parameter relating inertial and surface tension forces in a fluid flow, Consider a droplet of water where the Weber number is defined as: Calculate the Weber number We. pV²d We = Type your answer.. The following parameter values are measured and determined with 95% confidence: p = 1.000 + 0.008 V = 5.0 + 0.1 d = 1.000 + 0.025 mm (milimeters) 20 o = 0.072 + 3% Calculate the absolute uncertainty in the Weber number Uwe
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- The drag on an airplane wing in flight is known to be a function of the density of air (), the viscosity of air(), the free-stream velocity (U), a characteristic dimension of the wing (s), and the shear stress on the surface of the wing (s). Show that the dimensionless drag, sU2, can be expressed as a function of the Reynolds number, Us.The conduction heat transfer in an extended surface, known as a fin, yields the following equation for the temperature T, if the temperature distribution is assumed to be one-dimensional in x, where x is the distance from the base of the fin, as shown in figure: To Fin >X T(x) h,T Heat Loss d²T_hp (T-T) = 0 dx² ΚΑ dT dx = 0 Here, p is the perimeter of the fin, being 2R for a cylindrical fin of radius R; A is the cross-sectional area, being R2 for a cylindrical fin; k is the At x = 0: T = T₁ dT At x=L: :0 dx thermal conductivity of the material; T is the ambient fluid temperature; and h in the convective heat transfer coefficient. The boundary conditions are as follows: where L is the length of the fin. Solve this equation to obtain 7(x) by using Euler's method for R=1cm, h= 20 W/m².K, k = 15 W/m-K, L = 25 cm, T₁ = 80°C, and T = 20°C.At a sudden contraction in a pipe the diameter changes from D, to D2. The pressure drop, Ap, which develops across the con- traction is a function of D, and Dz, as well as the velocity, V, in the larger pipe, and the fluid density, p, and viscosity, u. Use D, V, and u as repeating variables to determine a suitable set of dimensionless parameters. Why would ti be incorrect to include the velocity in the smaller pipe a sa nadditional variable?
- Question 3 The power, P, to drive an axial pump is in a function of density of fluid, p, volumetric flow rate, Q, pump head, h, diameter of rotor, D, and angular speed of rotor, N. (a) (b) (c) P PDS N3 Verify that - is a dimensionless group. Determine the remaining pi group and perform dimensional analysis. Define geometric similarity and dynamic similarity. Categorize the pi group obtained from part (b) as geometric similarity or dynamic similarity, respectively.In this lab we will drop a steel ball (Psteel = 8000 kg/m³, rball = 2.18 x10³ m) through the air (Nair = 1.8 x105 Pa.s, Pair = 1.29 kg/m³), and through a viscous soap solution (Nsoap = 9.0 Pa.s [you will measure this number in the lab, but use this number for the prelab], Psoap = 1000 kg/m³). %3D 1 Pa = 1 N/m?. Calculate the terminal speed of the ball falling through the air, assuming that inertial drag is the dominant contributor. (For a sphere CD = and A is the area of the circle of radius r of the ball). Neglecting drag, estimate the time in seconds it takes for the steel ball to reach the terminal speed found in part 2 (i). Neglecting drag, estimate how far the ball would have travelled before reaching its terminal speed and comment on whether it is reasonable to neglect drag when studying the motion of this ball as it falls through the air from rest from the top of a 30 cm tall beaker or even from the ceiling of the room. Neglecting drag it would take 36 m to reach the terminal…4 Discharge, Q through a venturimeter depends on the following variable Inlet pipe diameter - D Throat diameter - d Pressure drop across the venturimeter - Ap Fluid density - P Dynamic viscosity - µ Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenon 5 The droplet size, D produced by a liquid spray nozzle depends on the following variable Nozzle diameter - d Jet velocity - U Fluid density - p Dynamic viscosity – u Surface tension - o Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenon
- 2. Experimental measurements of relationship between velocity gradient and shear stress for different liquids are shown in the table given below. a) Plot the data on Excel and determine the fluid types. (Show your graph!) b) Which model do you use to describe the data? Specify the ranges of values for the coefficients. Velocity gradient Shear stress Fluid A Fluid B Fluid C 0.2 2.60 7.80 61.55 0.5 5.80 17.40 63.67 0.95 10.51 31.53 66.45 1.4 14.52 43.56 69.30 1.9 21.02 56.75 72.89 2.45 28.22 64.91 77.60 3.05 31.50 69.30 80.38 3.7 38.91 71.98 84.50 4.35 45.21 76.86 88.81 5.05 51.71 80.15 93.78PROPAGATION OF ERROR You are tasked to supervise the design of 0.5MW wind turbine to be constructed in a Wind Farm in Pililla, Rizal. Suppose the design criteria are as follows: The air density as surveyed after 2 year period averaged at 1.225 kg / cubic meter. The sweeping diameter of the rotor blades is 125m, and the anemometer reading in the area amounts to 4.2m/s on a 2 year period of survey. What is the theoretical power output of the turbine assuming 100% efficiency of operation? Your answer must be in kW and in two decimal places with correct signs. In the previous problem, if the diameter measurement is off by 0.1m and the anemometer reading is also fluctuating by 0.05m/s and if the error measurement for theoretical power output must be limited to 3%, WHY OR WHY NOT should you accept the design? * Show complete solution in paper.1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance through the water V, acceleration due to gravity g, the angular speed of the propeller w, the water pressure 2, and the water viscosity . You want to find a set of dimensionless variables on which the thrust coefficient depends. In other words CT = Fr pV2D² = fen (T₁, T₂, ...Tk) What is k? Explain. Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V.
- b) The following shear stress – shear rate behavior was observed. Shear rate (Seconds-1) Shear Stress (dynes/cm?) 20 11 30 15.2 40 19.1 50 22.9 60 26.5 1. Make a plot of shear stress (ordinate) vs shear rate (abscissa) on log-log paper. 2. Can the fluid behavior be accurately modeled by the Newtonian, Bingham plastic, or Power law model?The power P required for operating a pump depends on the diameter of the pump D, the pressure rise Ap across the pump, the fluid density p, the fluid viscosity and the Theorem, and D, Q and p as the repeating variables, the dimensionless group associated with μ is given by volume flow rate Q through the pump. Using Buckingham's μDªQbpº. Determine the values of a, b and c. 1. [0.99, 1.01 2. [-1.01, 0.99 3. [-1.01, -0.99 a= b = C=The Reynolds number is a dimensionless group defined for a fluid flowing in a pipe as Re = Duplu where Dis pipe diameter, u is fluid velocity, p is fluid density, and u is fluid viscosity. When the value of the Reynolds number is less than about 2100, the flow is laminarthat is, the fluid flows in smooth streamlines. For Reynolds numbers above 2100, the flow is turbulent, characterized by a great deal of agitation. Liquid methyl ethylketone (MEK) flows through a pipe with an inner diameter of 2.067 inches at an average velocity of 0.48 ft/s. At the fluid temperature of 20°C the density of liquid MEK is 0.805 g/cm? and the viscosity is 0.43 centipoise [1 cP = 1.00 x 10-³ kg/(m-s)]. Without using a calculator, determine whether the flow is laminar or turbulent. Show your calculations.