the drag is given by FD-3nVd, where is the air viscosity. Find the maximum speed starting from rest, and the time it takes to reach 95 percent of this speed. Plot the speed as a function of time.
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- Ex. The force required to tow a 1:30scale model of a motor boat in a lake at a speed of 2m/s is 0.5 N, Assuming that the viscosity resistance due to water and air is negligible in comparison with the wave resistance, calculate the corresponding speed of the prototype for dynamically similar conditions. What would be the force required to propel the prptype at that velocity in the same lake? Ans.: 10.95m/s, 13500NProblem Solving: IJA car is fraveling at the speed Vo on a Tevel road. After the brakes ote applied at t = 0, the motion con be approximated by x = where x is the distance traveled in mcters and t is the time in seconds. Find: (a) Find the value of Vo straight, %3D %3D 100%A l, l. exercisec sheet.pdf -> Q7: Find the value of mass (mo) to move the mass 150 lb. downward the surface T 150 Ib mo H=03 20 Q8: The acceleration of a particle as it moving along a straight line is given by a = 2t-1 m/s. Where t is in seconds. If s = 1 m and v = 2 m/s where t = 0. Determine the particles velocity and position when t = 6s. also determine the total distance the particle travels during this time period. Q9: The van is travelling at 20 km/hr when the coupling of the trailer as A fails. If the trailer has a mass of 250 kg and coasts 45m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop. Q10: The double inclined plane supports two blocks A and B. each having a weight of 10 lb. If the coefficient of kientic friction between the blocks and the palne is uk = 0.1, determine the acceleration of each block. II
- The Reynold's number of a sphere falling in air is 1E6. If the sphere's radius is 1ft, what is its velocity? Density of air is 0.00234 slug/ft³ and viscosity of air is 3.8E-7 lbf-sec/ft²A. 2.5 ft/sB. 5.1 ft/sC. 40.6 ft/sD. 81.2 ft/s03:31 Given-Assign... External Problem 2: Dimensional analysis and similarity 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: PND? and a, = 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 750 kg/m 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. IN =1 kgm6.10 A sphere advancing at 1.5 m/s in a stationary mass of water experiences a drag of 4.5 N. Find the flow velocity required for dynamic similarity of another sphere twice the diameter, placed in a wind tunnel. Calculate the drag at this speed if the kinematic viscosity of air is 13 times that of water and its density is 1.25 kg/m³. Ans. (9.75 m/s, 0.951 N)
- A2) In order to solve the dimensional analysis problem involving shallow water waves as in Figure 2, Buckingham Pi Theorem has been used. h Figure 2 Through the observation that has been done, the wave speed © of waves on the surface of a liquid is a function of the depth (h), gravitational acceleration (g), fluid density (p), and fluid viscosity (µ). By using this Buckingham Pi Theorem: a) Analyze the above problem and show that the Froude Number (Fr) and Reynolds Number (Re) are the relevant dimensionless parameters involve in this problem. b) Manipulate your Pi (1) products to get the parameter into the following form: pch := f(Re) where Re = Fr = c) If one additional primary variable parameter involve in this proolem such as, temperature (T). Discuss on the Pi (m) products that can be produce and explain why this dimensional analysis is very important in the experimental work.L. y X VA A VB PLANE OF CONTACT BY UBC Engineering On an air hockey table, two pucks of identical mass collide in the middle of the rink. Puck A had an initial m velocity vA 1.9? and puck B had an initial velocity vB = 3.2j The plane of contact can be thought of as a line angled 0 = 34° above the x-axis. If the coefficient of 0.5 between the pucks, what are the velocities of the pucks after the impact? || m according to the x-y axis shown. restitution is e =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
- What is the volume of 92.4 grams of chlorine gas that is at a temperature of 46° C and a pressure of 694 mmHg? (Chlorine, R = 62.4 L- mm Hg/mole K and MW = 70.906 g/ mol) Computation: Show your Solution A lump of ice falls from an airplane as it comes into land. If the ice hits the ground with a vertical speed of 85m/s, what was the height of the plane when the ice fell off? (Assume that friction can be ignored.)C1 (a) A plate 0.05mm distant from a fixed plate moves at 1.15 m/s and required a force per unit area of 2.2 N/m2 to maintain this speed with using an oil of specific gravity 0.75. Find the dynamic viscosity and kinematic viscosity of the fluid between the plates. C1 (b) Calculate the specific weight, density, and the specific gravity of a liquid having a volume of 665000 cm3 and weight of 72 kN find : C1 (a) 1_The dynamic viscosity of the fluid (in Centipoise) 2_The kinematic viscosity of the fluid (in stokes) C1 (b) 3_Specific Weight in (N/m3) 4_Density of liquid (in kg/m3) 5_Specific gravity of liquidHw.1 1. With a starting velocity of 60 m/s, a tiny projectile is launched vertically downward into a fluid medium. The projectile decelerates by a = m/s? due to the fluid's drag resistance, where v is measured in m/s. Calculate the projectile's velocity and position 4 s after it is fired.