0.023 0.2 DG where C, is heat capacity, Btu lb¯ °F'; µ is viscosity, lb h ft"; k is thermal condu Btu h ft2 (°F ft)1; D is pipe diameter, ft; and G is mass velocity per The Colburn equation is dimensionally consistent. What are the units and dimensic unit area,
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- Ql: The viscosity in industrial measurement continue to use the CGS system of Lunits, since centimeters and grams vield convenient numbers for many fluids. The absolute viscosity () unit is the poise, I poise = 1 gtem. s). The kinematic viscosity (v) unit is the stohes, I stokes = 1 em /s. Water at 20C has u = 001 poise and also V= 0.01 stokes. Express these resalts in (a) SI and (h) BG tanits.Thermal conductivity k is a measure of the ability of a material to conduct heat. For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed as: Q=-kA.dT/dx where ?̇ is the rate of heat transfer and A is the area normal to the direction of heat transfer. Determine the primary dimensions of thermal conductivity (k). Look up a value of k and verify that its SI units are consistent with your result. Write a set of primary SI units for k.Q(2) Complete the blank cells in the following table of properties of steam. In the last column describe the condition of steam as compressed liquid, saturated mixture, superheated vapor, or insufficient information; and, if applicable, give the quality. Р (кра) T ('C) v, m'/kg u, KJ/Kg Phase description 300 35 130.24 313.22 135 600 1.34139 275 0.500 600 3090
- 1- The thrust (P l ) of a propeller depends upon diameter (D); speed (u) through a fluid density (p); revolution per minute (N); and dynamic viscosity (u) Show that: P = (p D² u²) f P Du [; where fis any function.(6) A dimensionless group called the Reynolds number is defined for a flow in a pipe or tube DV p NRe %3D uV/D Where V is the average velocity in the pipe, p is the fluid density, u is the fluid viscosity, D is the tube diameter. The second form of the group indicates that it is a ratio of the convective (turbulent) momentum flux to the molecular (viscous) momentum flux, or the ratio of inertial forces (which are destabilizing) to viscous forces (which are stabilizing). When viscous forces dominate over inertial forces, the flow is laminar and fluid elements flow in smooth, straight streamlines, whereas when inertial forces dominate, the flow is unstable and the flow pattern break up into random fluctuating eddies It is found that laminar flow in a pipe occurs as long as the value of Reynolds number is less than 2000. Calculate the maximum velocity and the corresponding flow rate (in cm'/s) at which lamina: tlow of water is possible in tubes with the following diameters: 0.64, 1.27,…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.
- In medical literatures, local blood perfusion rate is typically presented as xx ml/(min 100g tissue), in another word, it represents xx ml of blood supplied to a tissue mass of 100 g per minute to satisfy its nutritional needs. As we learned from the course lectures, the local blood perfusion rate appearing in the Pennes bioheat equation is in a unit of 1/s, or can be interpreted as xx ml of blood supplied to a tissue volume of 1 ml per second. The following lists the blood perfusion rates in various organs or structures in a human body from medical textbooks: brain (50 ml/(min 100g tissue)), kidney (35 ml/(min 100g tissue)), and muscle at rest (3 ml/(min 100g tissue)). Please convert the above local blood perfusion rates into values with the unit of 1/s, therefore, they can be used in the Pennes bioheat equation. The tissue density in a human body is 1050 kg/m³.The heat flux for stable film boiling on the outside of a horizontal cylinder or sphere of diameter D, in m, is given below. What should be the value of "n", for the equation above to be dimensionally consistent? Use dimensional analysis: q=heat flux, W m² W k = thermal conductivity of vapor, 'm °C hgf - [g kỷ Pv(P₁ − Pv)[hfg + 0.4 Cpv (Ts − Tsat)]] à = Cf MyD (Ts - Tsat) Pv = density of vapor, P₁ = density of liquid,- kg m³ kg 'm³ Cpv = enthalpy of vaporization, kg g = gravitatioinal acceleration, C = experimental constant, dimensionless m J kg °C Ts = surface temperature of the heater, °C Tsat = saturation temperature of vapor, °C kg Hv = viscosity of vapor, ms = specific hear of vapor, (Ts - Tsat)Use the following TTT Diagram for the following questions: 800 A 1400 -Eutectoid temperature 700 1200 600 1000 500 800 400 600 300 Mistart) 200 50% 400 M+A M(50%) M(90%) 100 200 10-1 10 102 103 10 105 Time (s) Temperature ("C) Termperature (°F)
- l .ll O 92 15:25 moodle.nct.edu.om/mod/ 11 P Flag question Calculate the density, weight density, specific mass of two liters of a fluid of weighs 5 kg (ENTER ONLY THE VALUES IN THE BOXES BY REFERRING THE UNIT GIVEN IN BRACKETS) density of fluid (unit in kg/m3) : %3D weight density of fluid is (Unit in N/m³) specific mass (unit in m3/kg) = specific gravity = Question 8 Not yet answeredDesigning safe boilers depends on knowing how steam behaves under certain changes in temperature and pressure. Steam tables, such as the one below, are published giving values of the function V = f(T, P) where V is the volume (in cubic feet) of one pound of steam at a temperature of T (in degrees Fahrenheit) and pressure P (in pounds per square inch). T//P 480 500 520 540 20 22 24 26 27.85 25.31 23.19 21.39 28.46 25.86 23.69 21.86 29.06 26.41 24.20 22.33 29.66 26.95 24.70 22.79 a) Find the tangent plane to V = f(T, P) for T near 520°F and P near 24 lb/in². [Hint: Use the tables to approximate your partial derivatives and recall the equation of our tangent plane is: V = VT(T − To) + Vp(P - Po) + f(T, P) ] b) Use the tangent plane to estimate the volume of a pound of steam at a temperature of 525°F and P near 24.3 lb/in².a)Weber number (We) represents the ratio of disruptive hydrodynamics forces to the stabilizing surface tension force. It is an important dimensionless parameter applied during the analysis of thin film flows, which examines the ratio between inertia force and surface tension force acting on a fluid element. Using The Buckingham Pi Theorem, generate the formula for We. We is a function of fluid density (ρ), fluid velocity (v), characteristic length (l) and surface tension (σs), which can be mathematically written as: ?? = ?(?,?,?,??) b)Froude number (Fr) is an important dimensionless parameter used in open channel flow. Give the physical and mathematical definition of Fr. Prove that Fr is dimensionless.