Q2:A) An experimental text program is being set up to calibrate a new flow meter. The flow meter is to measure the mass flow rate of liquid flowing through a pipe. It is assume the mass flow rate (m) is a function of the pressure difference (AP)across the meter, diameter of the pipe (D), viscosity of the fluid (μ), and the density of the fluid (p). Using the dimensionless analysis, find the 7-groups for this case study.
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- Q2:A) An experimental text program is being set up to calibrate a new flow meter. The flow meter is to measure the mass flow rate of liquid flowing through a pipe. It is assume the mass flow rate (m) is a function of the pressure difference (AP)across the meter, diameter of the pipe (D), viscosity of the fluid (μ), and the density of the fluid (p). Using the dimensionless analysis, find the 7-groups for this case study.A) An experimental text program is being set up to calibrate a new flow meter. The flow meter is to measure the mass flow rate of liquid flowing through a pipe. It is assume the mass flow rate (m) is a function of the pressure difference (AP)across the meter, diameter of the pipe (D), viscosity of the fluid (μ), and the density of the fluid (p). Using the dimensionless analysis, find the-groups for this case study.Q2:A) An experimental text program is being set up to calibrate a new flow meter. The flow meter is to measure the mass flow rate of liquid flowing through a pipe. It is assume the mass flow rate (m) is a function of the pressure difference (AP)across the meter, diameter of the pipe (D), viscosity of the fluid (4), and the density of the fluid (p). Using the dimensionless analysis, find the-groups for this case study.
- c) When small aerosol particles move through air or water, the Reynolds number is very small (Re < 1). Such flows are called creeping flow. The aerodynamic drag on an object in creeping flow is a function only of its speed, V some characteristic length scale, L of the object and fluid viscosity, µas indicated in Figure 11. Use dimensional analysis to generate a relationship for Fp as a function of the independent variables. The dimensions of Fp are MLT2. FD L Figure 11Ql: 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.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=
- a) Vortex shedding is a common fluid flow problem across bluff bodies. The design of buildings and bridges take into account the analysis of vortex shedding phenomena to avoid the occurrence of resonance, where the natural frequency of the body matches the vortex shedding frequency. In this analysis, the following parameters are found to be important: velocity of flow (V), density of fluid (p), hydraulic diameter of the duct (D₁), dynamic viscosity of fluid (u), width of body (B) and the vortex shedding frequency (n). Using the method of repeating variables, find the non-dimensional relationship governing the phenomena.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?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.
- 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.Parts for each product Homework 1 n produce dryer plant Can for each product castiens Then each product is assembled in its dedicated washing and dryer A machines. Difterent are manufactured by press and motor ly sechon. The the monthly capacity of different sections are: washing machine or looo dryer machine Press section: 100 - Motor section: 1600 washing machine or 7o00 drjer machine machine assembly line: goo0 machine washing druer machine assembly line: 5000 machine washing 1, profit for each unct of washing and dryer machines is 270 and 300 respectively. Formulate a linear programming problem for Find ing how many washing and dryer machines should be produced many washing to maximize total plant's profit. 2.A A Post Company need to transfer 30000 boxes with two each truck presented of olifferent trucks. Chavactenistics problem for The table below. Formulate a linear programming each truck to optimum nunber of minimIze total Cost.Volumetric flow rate, Q, of a pump is a function of impeller diameter d, fluid velocity V, pressure difference DP, fluid density r and viscosity m. a)Determine dimensionless P groups. b)A test is to be performed for a large pump that delivers 1.5 m3 /s of water from 40 cm diameter impeller with pressure rise of 400 kPa. For the test, a model with an 8 cm diameter impeller is to be used. What flow rate should be used and what would be the pressure rise in model pump. Note: The model fluid is water at same temperature as the water in the prototype.