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 pand viscosity H, the velocity V and the cross section length of the airplane D. a) Use dimensional analysis to prove that: F and 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?

Acording to Darcy law, P is a pressure, V is a velocity, D is a diameter, g is acceleration gravity, f is dimensionless coefficient. Is the equation dimensionaly consistent?

The pressure difference ∆p produced by a water pump, and the power P required to operate it, each depend on the size of the pump, measured by the diameter D of the impeller, the volume flow rate ˙q, the rate of rotation ω, the water density ρ and dynamic viscosity µ. (a) Express the non-dimensional pressure difference and power as separate functions of the other non-dimensional groups. (b) Tests on a model pump are performed at 0.5 × full scale, at a rotation rate that is 2 × the full-scale value. To achieve dynamic similarity in the model test: (i) what would the volume flow rate of the water need to be in the model test compared to the full-scale? (ii) What would the pressure difference be compared to the full scale? (iii) What would the power consumption be relative to the full scale?  

help

Using II-Theorem method to Express (n) in terms of dimensionless groups.The efficiency (n) of a fan depends upon density (p), and dynamic viscosity (u), of the fluid, angular velocity (@), diameter of the rotator (D), and discharge (Q). Q3/ A petroleum crude oil having a kinematics viscosity 0.0001 m?/s is flowing through the piping arrangement shown in the below Figure,The total mass flow rate is equal 10 kg/s entering in pipe (A) . The flow divides to three pipes ( B, C, D). The steel pipes are schedule 40 pipe. note that the dynamic viscosity 0.088 kg/m.s. Calculate the following using SI units: 1- The type of flow in pipe (A). 2- The mass velocity in pipe (B) GB. 3- The velocity in pipe (D) Up. 4- The Volumetric flow rate in pipe (D) QD. 5- The Volumetric flow rate in pipe (C) Qc. Og = 2o mm Ug = 2UA Perolenm crude oIL A ma = 1o Kg/s O = 5o mm mic = ? Go = 7000 k9/m.s Nate that!- O, = 30 mm. D:0iameter. U:velocity G mass velocity mimass How vate

A student team is to design a submarine for a design competition. The overall length of the prototype submarine is 4.85 m. The prototype submarine is expected to moves through freshwater in the lake at 0.440 m/s. The student team builds a one-fifth scale model to test in their university's wind tunnel. Calculate the wind tunnel air speed in order to achieve similarity with the prototype submarine. For water at T= 15 °C and atmospheric pressure, the density is p = 999.1 kg/m³ and the dynamic viscosity is µ = 1.138 x 10³ kg/m-s. For air in the wind tunnel at T= 25 °C and atmospheric pressure, the density is p= 1.184 kg/m³ and the dynamic viscosity is µ = 1.849 x 10-$ kg/m's.

The following equation may be used to estimate the take-off ground run for an aircraft: Equation has been attached as an image. Calculate the take-off ground run, from a runway at ISA-SL conditions, for a twin engine aircraft for which the following data may be assumed Aircraft lift-off speed 155 knots Max take-off gross weight 220 tonnes Wing planform area (S) 358 m Wing CL (t/o flaps deployed, a = 0) 1.1 Wing span 53.18 m Oswald efficiency factor, e 0.7 KGE = CD(IGE) / Co(OGE) 0.4 Co sum (fuselage, wing, tailplane and nacelle) 0.015 Co for undercarriage 0.021 Co for flaps at taking-off setting 0.0073 Coefficient of rolling friction, u 0.02 Engine thrust (assumed constant) 310 kN per engine It may be assumed that 1knot = 0.51444 m/s   It may be assumed that 1knot = 0.51444 m/s

CH, CQ and n are functions of CP. Draw the dimensionless performance curves of the turbine on a single graph by makingthe necessary scalings. (Fit the curve by using the excel program for drawing. Also give the values you used for plotting inthe table) ÖN=5

20 4. An airship is to operate at 20 m/s in air at standard conditions (p 1.225 kg/m³, p 101,300 Pa). A model is constructed to scale and tested in a variable-pressure wind tunnel at the same air temperature to = determine the drag. GOOD YEAR The Goodyear Blimp is an example of an airship. (a) What criterion should be used to determine dynamic similarity? (You may assume that roughness is not important for this problem.) (b) If the model is tested at 20 m/s, what pressure should be used in the wind tunnel? (c) If the model drag force is found to be 250 N, what will be the drag of the full-scale airship?

Answer all the questions 1) Using dimensional equations, convert: 700 m* /(day. kg) to cem* /(min. g). 2) Convert 210 X 10 kJ/min to hp 3) Calculate the weight in lbr of a 30.0-lbm object. 4) Calculate the mass in kg of an object that weighs 25 Newton. 5) The density of a fluid is given by the empirical equation: p = 70.5 exp(8.27 x 10-7P) where p is density (Ib/ft) and Pis pressure (lb,/in.?). (a) What are the units of 70.5 and 8.27 x 10-7? (b) Calculate the density in g/cm for a pressure of 9.00 x 10 N/m?. 6) The vapor pressures of 1-chlorotetradecane at several temperatures are tabulated here. T(C) 98.5 131.8 148.2 166.2 199.8 215.5 p* (mm Hg) 1 5 10 20 100 60 Use two different method to estimate the value of P' at T = 190 °C (7) The specific gravity of gasoline is approximately 0.70. a- Determine the mass (kg) of 50.0 liters of gasoline. b- The mass flow rate of gasoline exiting a refinery tank is 1150 kg/min. Estimate the volumetric flowrate in liters/s.