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- The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND? b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/m² and the dynamic viscosity is 0.2 N.s/m². For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s/m². kg.m IN =1A dam spillway is to be tested using Froude scaling with a 1:20 model. The model flow has an average velocity of 0.7 m/s. What is the velocity of prototype?For the drag force of an Aerobee rocket, D=0.00056v (Ib], obtain a linear model near v = 800 ft/sec and find the velocity below 800 ft/sec that the model prediction error becomes greater than 2%. Enter an answer in a whole number in ft/sec.
- A fighter aircraft is to operate at 200 m/s in air at standard conditions (p= 1.2 kg/m³). A model is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the same air temperature (same air viscosity) to determine the drag force. The drag force Fp is a function of the air density p and viscosity µ, the velocity V and the cross section length of the airplane D. a) Use dimensional analysis to prove that: F, and PV²D² pVD What are these two dimensionless numbers? b) If the model is tested at 50 m/s, what air density should be used in the wind tunnel? Comment the result and give a recommendation. c) If the model drag force is 250 N at 50 m/s, what will be the drag force of the prototype? Lift force 200 m/s Drag force1. 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.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.
- A sphere is moving in water with a velocity of 1.6 m/s. Another sphere of twice the diameter is placed in a wind tunnel and tested with air which is 750 times less dense and 60 times less viscous (dynamically) than water. The velocity of air that will model dynamically similar conditions isUnder a laminar flow, the liquid flows through small holes. It has a triangular cross-section, width b and length L, where the volumetric flow rate Q of the flow is a function of viscosity. ,pressure reduction per unit length p/L and width b 1) Use the PI theory to write the relationship as a dimensionless variable. 2) if the width b is doubled by viscosity And the pressure drop per unit length p/L is the same. I want to know how the flow rate Q will change.i [ 4=l Fal @ docs.google.com/forms () Iromgenerai norary. - O true O false Static structural simulation needs at least three boundary conditions * @ True O False Study —state thermal needs maximum one boundary conditions * O true @ False Ansys coordinate system is global n coordinate system. O O >
- 03: The power output (P) of a marine current turbine is assumed to be a function of velocity U, blade length L, angular velocity w, fluid density p and kinematic viscosity v. (a) Use dimensional analysis to show that, =f,4 (b) In a full-scale prototype the current velocity U = 2.0 m/s and the angular velocity is o = 15 rpm. A 1:10 scale laboratory model is to be tested in fluid of the same density with angular velocity w = 60 rpm. What velocity should be used in the model tests? (c) If the power output in the model tests is 200 W, what power output would be expected in the prototype? Answer: (a) f,), (b) Um= 0.8 m/s , (c) P,= 312 kW %3D (pu³L2)3. Problem Estimate the frictional resistance Rp for a container ship using the ITTC 1957 model-ship correlation line Equation (2): 0.075 CF [ log,,(Re) – 21 The ship has the following particulars: Full scale ship data length between perpendiculars Lep length in waterline length over wetted surface 195.40 m Lwz Los For the wetted surface S you can use the following formula by Kristensen and Lützen (2012) derived for container ships. 200.35 m 205.65 m breadth B 29.80 m draft T 10.10 m 37085.01 m3 S = 5 + Lw. T 0.995 displacement design speed Again, use the most up-to-date ITTC water properties sheet for density and kinematic viscosity. V 21.00 knThe 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.