Actual airflow past a parachute creates a variable distribution of velocities and directions. Let us model this as a circular air jet, of diameter half the parachute diameter, which is turned completely around by the parachute, as in Fig. P3.106. (a) Find the force F required to support the chute. (b) Express this force as a dimensionless drag coefficient,
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Fluid Mechanics
- Q 3. A submarine of length 160 m, average diameter of 15 m moves through seawater with kinematic viscosity 1.5x10-6 m²/s and density 1025 kg/m3 at 9.5 m/s. Estimate the power needed to overcome the drag force. Consider the submarine as a fat plate that has the same surface area as the submarine.arrow_forwardA horizontal circular jet of air (pair plate as shown below. The air jet has a velocity V; = 60 m/s and the air jet has a diameter Dj = 40 mm. An anchoring force FA is holding the plate in its stationary position. This entire system is open to the atmosphere. 1.23 kg/m³) strikes a stationary flat Gravity is into / out of the page ... gravity will not be important here! The air velocity magnitude remains constant ( |Vi| = |V2| = |V3| ) as the air flows across the plate surface (this means there are no shear stress effects). Hint align your coordinate system with V3, V2, and FA. ... V2 D : = 40 mm V; = 40 m/s 30° V3 FA (3.a) What is the magnitude [ N ] of the anchoring force FA? (3.b) What fraction [ % ] of the total mass of air leaves at V2? Now we will change the problem a little. Allow the plate to move to the right with a constant speed of 18 m/s. You should realize that this will mean that the anchoring force is reduced from the answer you found in (4.a). Please place your observer…arrow_forwardP1.59 A solid cylinder of diameter D, length L, and density Ps falls due to gravity inside a tube of diameter Do. The clear- ance, Do - D<< D, is filled with fluid of density p and viscosity µ. Neglect the air above and below the cylinder. Derive a formula for the terminal fall velocity of the cylin- der. Apply your formula to the case of a steel cylinder, D = 2 cm, Do = 2.04 cm, L = 15 cm, with a film of SAE %3D 30 oil at 20°C.arrow_forward
- P3.48 The small boat is driven at steady speed Vo by compressed air issuing from a 3-cm-diameter hole at Ve = 343 m/s and pe = 1 atm, Te = 30°C. Neglect air drag. The hull drag is kVo?, where k = 19 N · s/m². Estimate the boat speed Vo. %3D D= 3 cm Compressed V -E air Hull drag kVarrow_forwardA milkshake has fairly similar density to that of water (m s = 1200 kg/m3) but is far more viscous ( = 1kg/ms) (a) Say you try to drink a milkshake through a straw that is 30 cm long and 5 mm in diameter. Your lungs are capable of creating a vacuum pressure of 3000 Pa. (Vacuum pressure just means a pressure below that of the atmosphere, so plung = patm 3000 Pa.) You Önd that if you place the straw just at the surface of the liquid, you are unable to suck the milkshake through the straw, but if you push the straw deeper into the shake, you can. To what depth, d, would you need to push the straw in order to just start to sip the milkshake?(b) Suppose you push the straw to a depth of 10 cm and suck with a suction pressure of 3000 N/m2. What volume áow rate of milkshake can you produce through the strawarrow_forwardA viscous liquid of constant ρ and μ falls due to gravitybetween two plates a distance 2 h apart, as in Fig. P4.37. Thefl ow is fully developed, with a single velocity component w = w ( x ). There are no applied pressure gradients, onlygravity. Solve the Navier-Stokes equation for the velocityprofi le between the plates.arrow_forward
- 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?arrow_forwardIn some wind tunnels the test section is perforated to suckout fl uid and provide a thin viscous boundary layer. Thetest section wall in Fig. P3.33 contains 1200 holes of 5-mmdiameter each per square meter of wall area. The suctionvelocity through each hole is V s = 8 m/s, and the testsectionentrance velocity is V 1 = 35 m/s. Assuming incompressiblesteady fl ow of air at 20 8 C, compute ( a ) V 0 , ( b ) V 2 ,and ( c ) V f , in m/s.arrow_forwardA fl uid jet of diameter D 1 enters a cascade of movingblades at absolute velocity V 1 and angle β 1 , and it leaves atabsolute velocity V 2 and angle β 2 , as in Fig. P3.78. Theblades move at velocity u . Derive a formula for the powerP delivered to the blades as a function of these parameters.arrow_forward
- The lift on a spinning circular cylinder, in a freestream with a velocity of 10m/s, is measured as L, at standard sea level conditions and L, at an altitude of 10,000ft. (Assume that both cases generate the same circulation around the cylinder.) How do you compare L, and L2? Please choose one of the following alternatives: (1) L1 = L2 (ii) L1 > L2 (iii) L1 < L2 (iv) None of them O i O i O i O ivarrow_forward3.4 Specification of a laminar boundary layer profile as an inflow condition is often used in incompressible flow simulations. Let us consider the Blasius profile, which is a similarity solution for the steady laminar boundary layer on a flat plate. Fig. 3.25 Flat-plate laminar boundary layer Dv 2. Consider the streamfunction(with u = and v=- transform from (x, y) to (x, n), where n = y √ux/U% = Rex u(x, y) and a coordinate Using the above and a streamfunction in the form = √xUf(n), show that the governing equations can be reduced to ff" +2f"" = 0 with boundary conditions of f(0) = f'(0) = 0 and lim, f(n) = 1. This equation is referred to as the Blasius equation and its solution is known as the Blasius profile.arrow_forward6.6 The boundary layer thickness d at any section for a flow past a flat plate de- pends upon the distance x measured along the plate from the leading edge to the section, free stream velocity U and the kinematic viscosity v of the fluid. Show with the help of Rayleigh's indicial method of dimensional analysis that c (Ux/v) or %3Darrow_forward
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