O The power, W, generated by a certain windmill design depends upon its diameter, D, the air density, p, the wind velocity, V, the rotation speed, Q, and the number of blades n. By using velocity V, diameter D and density. " as the repeating variables, prove the dimensionless relationship is given by DV
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- Under 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.b) When a liquid in a beaker is stirred, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (o) of the whirlpool, fluid density (p), gravitational acceleration (g), and radius (R) of the container. Take o, p and R as the repeating variables.Q2 Consider a conical receiver shown in Figure 2. The inlet and outlet liquid volumetric flow rates are Fl and F2, respectiveily. ccorresponding radius in r) Figure 2 Conicul tank Develop the model equation with necessary assumption(s) with respect to the liquid height h. ii. What type of mathematical model is this? 1 R %3D Hint: Model: = F, – Fz, where the volume V=r h=nh, since = substitute V and Fz expressions and get the final form. %3D %3D %3D dt H.
- Energy of a Roller Coaster Car 500 450 400 350 --- 3 300 250 E 200 150 100 50 6 8 10 Time (s) Mechanical Energy ....... Potential Energy -- Kinetic Energy This graph shows different types of energy for a roller coaster car that starts at the top of a large hill and goes down to its lowest point at 6 s. According to the graph, what is the most likely relationship between height and potential energy? Your answer: They are directly related. They are inversely related. There is no relationship between the two. There is not enough information for a conclusion.2. Consider a large industrial fan where the input power, W, depends on the fan impeller diameter, D, fluid viscosity, u, fluid density, p, volumetric flow rate, Q, and blade rotational rate, w. a) What are the appropriate dimensionless groups (Pi terms) if we consider D, p, and Q as repeating (reference) variables. b) If a model fan has a diameter, Dm, that is half of the prototype fan diameter, D, , what should be the ratio of the model blade rotation rate, Wm , to prototype, wp, to have dynamic similitude. Assume the same fluid (air) properties; that is viscosity and density are the same in both cases.b) The variation in the experimental density of water, p, with temperature T, in the range of 20°Cfet), force force, f 10 Newt. m2 f k, 10sec m, = 10 kg, ma= 20 kg , b= 20 Newton m/sec k, = 30 Newton kz = 60 Newton z, and z are measured with respeet to eguilibrium conditions and all imitial conditions are zero, 1) Write the Newton's second Lau for m, amd m2 2) Derive a statespace represrentation of the conditions : eystem fallowing 2a) only z, is measured 26) only z, is measured 2c) (2,-z,) is measured. un der 3) Derive the following transfor fumetione fG) z,(5) Go G,6) ? G6) ? 4) Describe a mechanical device that can be used to implement the external force fee) as shoun'a bove. 5) Using (Csim) function of MATLAB, plot z,(t), 2, (t)- =, (+)] Zz (t) andThe power P generated by a certain windmill design depends on its diameter D, the air density p, the wind velocity V, the rotation rate w and the number of blades n. a) Write this relationship in dimensionless form. A model windmill of diameter 50 cm develops 2.7 kW at sea level when V=40 m/s and when rotating at 4800 r/min. b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude? c)What is the appropriate rotation rate of the prototype?Independent variables in a turbomachine are the impeller diameter, D, angular speed, ω, and fluid viscosity and density. Dependent properties are volumetric flow rate, Q, head, H (energy per unit mass), and power input, P. Use ρ, ω, and D as repeating variables in a dimensional analysis. a) Determine the dimensionless ratios that characterize this problem. b) Under what conditions will flows in two different machines be similar? c) Determine the speed of operation for machine 2 for the same flow as machine 1 if D2/D1 = 2 and viscous effects are unimportant. What will be the head ratio under these conditions? Note:hand written solution should be avoided.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.YouTube Mall Over... Leeds International... M1 Questions by To... Question Completion Status: QUESTION 2 A car of mass 750 kg moves along a stretch of road which can be modelled as a line of greatest slope of a plane inclined to the horizontal at 30°. As the car moves up the roa for 500 m its speed reduces from 20 ms-¹ to 15 ms-¹. Calculate: a the loss of kinetic energy of the car 65,625) 66,625 67,625) O 68,625)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.SEE MORE QUESTIONS