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A bird is flying in a room with a velocity field of
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Fluid Mechanics: Fundamentals and Applications
- The two components of the velocity vector are given as Vx = –ay/(x2+ y2)1/2 and Vy = ax/(x2+ y2)1/2 where a is a constant in cm/s. Find the vorticity of a fluid element located at x = y = 1 cm. [Ans.: 1.41a k ].arrow_forwardAn aircraft is flying at a speed less than 100 meters per second in sea level. Which of the following statement is true? A. density changes are small and the flow can be regarded as incompressible B. the flow should be regarded as compressible since Mach number is less than 0.3 C. the flow should be regarded as compressible since Mach number is greater than 0.3 D. density changes are small and the flow can be regarded as compressiblearrow_forwardAn aluminum sphere of radius 0.5 mm falls through a viscous liquid of density 2700 kg/m3. It attains a constant terminal velocity of 1.5 cm/s. What is the viscosity of the fluid? a) 0.001 N.s/m2 b) 0.052 N.s/m2 c) 0.25 N.s/m2 d) none of thesearrow_forward
- A nuclear reactor is cooled by liquid sodium. The liquid sodium has the following properties: dynamic viscosity = 0.41 mPa·s, specific heat capacity = 1.2 kJ/kgK, thermal conductivity 82 W/mK. Which of the following statements is correct for this scenario? please explain A The thermal boundary layer is thicker than the hydraulic boundary layer. B Heat is transferred through the fluid more easily than momentum. C The velocity varies significantly from the surface to the thickness of the thermal boundary layer. D The hydraulic boundary layer is thicker than the thermal boundary layer.arrow_forwardfluid mechanics Water at 20°C is flowing through a horizontal nozzle at a flow rate of 0.005 m3/s. At the nozzle inlet, the diameter is 5 cm and the pressure is 200 kPag. The nozzle discharges freely to outside air. Determine the velocity of the water (in m/s) as it exits the nozzle. Assume negligible head losses through the nozzle. Round your answer to 2 decimal places.arrow_forwardFluid Mechanics A horizontal jet of water exits a nozzle with a uniform velocity of Vj = 20 m/s and area of Aj= 3 cm^2, and strikes a flat plate that moves to the right at velocity of Vc = 15 m/s. Upon impinging the plate, the jet splits into an equal upward and downward half-jet. (i.e. A1 = A2 = 0.5Aj). Neglecting gravity and viscous forces, determine the force (in both x - and y - directions) required to keep the plate moving at a constant velocity.arrow_forward
- 1) A steady, incompressible fluid flow through two identical pumps in series, the volume flow rate through the two pumps is equal to V1˙+V2˙. True or False 2) When calculating efficiency, equations for pump and turbine are the same, and both efficiencies should be less than 1. True or Falsearrow_forwardA pipe has an inside diameter of 4” at an inlet and an inside diameter of 2” at outlet. For an ideal fluid flow, the velocity is given as 1ft/s at an inlet. What is the flow velocity at outlet? A. 25 ft/s B. 0.5 ft/s C. 1.0 ft/s D. 2.0 ft/s E. 0.4 ft/sarrow_forwardCourse: fluid mechanics and Turbomachinery book reference: Dixon and Hall, “Fluid Mechanics and Thermodynamics of Turbomachinery, 7th ed.; Butterworth-Heinemann; Waltham, MA. 2014arrow_forward
- When a viscous, incompressible fluid enters a pipe of radius, R, its velocity is uniform and of magnitude U0. The fluid eventually becomes fully-developed, at which point it has a parabolic velocity profile described by the equation u(r) = Umax[ 1 − ( r/R )^2 ] , where r is the radial distance measured from the center line of the pipe. Determine an expression for the ratio of the max velocity of the fully-developed pipe flow to the uniform inlet velocity, Umax/U0. The fluid is flowing steadilyarrow_forwardComplete Solution please, thanks. 3. A vertical circular stack 30 m high converges uniformly from a diameter of 6 m at the bottom and 4.5 m at the top. Gas with a unit weight of 0.12 N per cubic meter enters the bottom of the tank with a uniform velocity of-assume values with decimals between 3 to 4 m per second- enters the stack. The unit weight increases by 7.5 percent every 2 meters. Find the velocity of flow at every 5 meters along the stack.arrow_forwardFor the flow of a viscous fluid, with the velocity V = f(x)g(y)h(z)i (where f, g, h are arbitrary functions), the following conditions are given: . The flow is adiabatic. • The quantities v = 2 and 3 = $ are constants. • The velocity circulation is conserved for the flow, irrespective of the values of vand 3. What is the general solution for the functions f, g, h?arrow_forward
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