For creeping flow over a three-dimensional object, the aerodynamic drag on the object does not depend on (a) Velocity, V (b) Fluid viscosity, ? (c) Characteristic length, L (d ) Fluid density, ? (e) None of these
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For creeping flow over a three-dimensional object, the aerodynamic drag on the object does not depend on (a) Velocity, V (b) Fluid viscosity, ? (c) Characteristic length, L (d ) Fluid density, ? (e) None of these
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- Mott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?The drag force (Fdrag) exerted by air on a moving car depends on a dimensionless drag coefficient (Carag), the specific volume of air (Vair), the velocity of the car (Var), and the frontal area of the car (Afront). (a) Based on unit considerations alone, obtain an equation for the drag force. Be sure to explicitly demonstrate that the final units are correct. (b) Explain, based on your equation, what happens to the drag force when each variable is changed in isolation. Indicate whether this predicted behaviour matches your intuition in each case.Consider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness ? , downstream distance x, free-stream velocity V, fluid density ? , and fluid viscosity ? . The number of primary dimensions represented in this problem is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5
- Consider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness ? , downstream distance x, freestream velocity V, fluid density ? , and fluid viscosity ? . The number of expected nondimensional parameters Πs for this problem is (a) 5 (b) 4 (c) 3 (d ) 2 (e) 1The drag of a sonar transducer is to be predicted, based on wind (Air) tunnel test data. The prototype is 1.5 m diameter sphere, is to be towed at 4.3 m/s in seawater. The model is 0.2 m diameter. Take: Air density = 1.2 kg/m, Air dynamic viscosity = 1.81 x 10$ Pa. s, seawater density = 1000 kg/m, seawater dynamic viscosity 1.813x 10 Pa s, If the drag of the model at these test conditions is 9.5 N, estimate the drag of the prototype in (N).Q.3 Air (density 1.2 kg/m3 and kinematic viscosity 15 centistokes) flows over a flat plate, at zero angle of incidence, at a velocity of 20 m/s. If Reynolds number at transition is taken as 2.5 x 105, maximum distance, from leading edge up to which the boundary layer remains laminar, is
- The drag coefficient CD is a nondimensional parameter and is a function of drag force FD, density ? , velocity V, and area A. The drag coefficient is expressed as (a) FDV2 /2ρA (b) 2FD / ρVA (c) ρVA2 / FD (d) FDA / ρV (e) 2FD / ρV2AA hydrofoil 51 cm long 4 m wide moves at 1m/s in water at temperature 20 C. Use laminar boundary theory to find,(a) The Drag force and Boundary layer thickness at the trailing edge of the hydrofoil.(b) What would be the effect on Drag force and Boundary layer thickness if water is replaced with CO2 at the same condition?1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?
- This exercise is part of a series of problems aimed at modeling a situation by progressively refining our model to take into account more and more parameters. This progressive approach is very close to whatwhat do professional scientists do! contextWe want to lower a suspended load in a controlled way, so that it hits the ground with a speed whose modulus is not too great. To slow down the descent, we added a resort behind the mass (A), Lasuspended load (B) is connected by a rope passing through a pulley to another mass (A), which slides on a horizontal surface with friction.InformationThe masses of loads A and B are known.The mass of the rope itself is negligible (very small compared to the loads).The pulley has negligible mass and can rotate without friction.Load B is initially stationary and is at a known height h.The surface on which mass A is placed is horizontal.There is friction under mass A: the kinetic friction coefficient u, is known.The rope attached to mass A is perfectly…The so-called Rocket Man, Yves Rossy, fl ew across the Alps in2008, wearing a rocket-propelled wing-suit with the followingdata: thrust = 200 lbf, altitude = 8,200 ft, and wingspan = 8 ft(http://en.wikipedia.org/wiki/Yves_Rossy). Further assume awing area of 12 ft2, total weight of 280 lbf, CDq = 0.08 for thewing, and a drag area of 1.7 ft2 for Rocket Man. Estimate themaximum velocity possible for this condition, in mi/h.In the study of turbulent flow, turbulent viscous dissipation rate ? (rate of energy loss per unit mass) is known to be a function of length scale l and velocity scale u′ of the large-scale turbulent eddies. Using dimensional analysis (Buckingham pi and the method of repeating variables) and showing all of your work, generate an expression for ? as a function of l and u′.