Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.12P
Consider a length of pipe bent into a U-shape. The inside diameter of the pipe is 0.5 m. Air enters one leg of the pipe at a mean velocity of 100 m/s and exits the other leg at the same magnitude of velocity, but moving in the opposite direction. The pressure of the flow at the inlet and exit is the ambient pressure of the surroundings. Calculate the magnitude and direction of the force exerted on the pipe by the airflow. The air density is
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As shown in the figure, water enters and leaves a U-shaped piece of pipe in the horizontal plane.The total absolute pressure at the flange number (1) is 200 kPa, and a mass flow of 40 kg/s is entering the pipe.On the flange number (2), the total pressure is 150 kPa and there is a mass flow of 30 kg/s from the pipe.The mass flow rate of 4 kg/s from the section (3) and 6 kg/s from the section (4) is thrown into the atmosphere at a pressure of 100 kPa.Working with relative pressures;Determine the total forces Rx and Ry at the two flanges attached to the pipe.
Note: Mass flow rate = Specific mass x Flow rate Flange, sealing of two machines or plumbing elementsgenerally standard for combiningIt is a construction element produced as Sections (1) and (2) are close enough to each other. For fluid entering and leaving the control volumeKinetic energy correction factor 1.035 and momentumThe flow correction coefficient is 1.025. Specific mass of water: ??? = 1000 ??/?3
Chapter 2 Solutions
Fundamentals of Aerodynamics
Ch. 2 - Consider a body of arbitrary shape. If the...Ch. 2 - Consider an airfoil in a wind tunnel (i.e., a wing...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the radial and...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - The velocity field given in Problem 2.3 is called...Ch. 2 - The velocity field given in Problem 2.4 is called...Ch. 2 - Is the flow field given in Problem 2.5...Ch. 2 - Consider a flow field in polar coordinates, where...
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- The power generated by a wind turbine is proportional to the cube of the wind velocity. Inspired by the acceleration of a fluid in a nozzle, someone proposes to install a reducer casing to capture the wind energy from a larger area and accelerate it before the wind strikes the turbine blades, as shown in Figure. Evaluate if the proposed modification should be given a consideration in the design of new wind turbines. The figure is attached as image. Thank you.arrow_forward1- A 2 m long conical tube is fixed vertically with its smaller end upwards. It carries liquid in downward direction. The flow velocities at the smaller and larger ends are 5m/s and 2m/s respectively. The 0.35(u₁-u₂)² pressure head at the smaller end is 2.5 m of liquid. If the loss of head in the tube is 2g (u, and u₂ being the velocities at the smaller and larger ends respectively). Calculate the pressure head at the larger end.arrow_forwardWater is flowing through a U-section pipe as shown in Figure 1.2. At flange (1) the total absolute pressure is 240 kPa, and water flows into the pipe at 42 kg/s. At flange (2), the total pressure measured is 190 kPa with a flow rate of 32 kg/s. At point (3) water discharges into the atmosphere at 90 kPa at a flow rate of 10 kg/s. The mass of the elbow and the water in it is 50 kg. Neglecting the momentum-flux correction factor, determine the net x- and z-force at the two flanges connecting the pipe. T0 kg/s 3 ст 32 kg/s- 10 cm 42 kg/s S cm Figure 1.2arrow_forward
- The increase in flow energy of a 10 ft3 of fluid passing a boundary of a system is 80,000 ft-lb. Determine the exit pressure if the inlet pressure is 100 psi.arrow_forwardWater flows in a 170 mm diameter pipeline (A) divides into two smaller pipelines, one being 100 mm in diameter (D) and the other being 80 mm in diameter (B). If the velocity in the 80 mm pipe (B) is 0.6m/s and that in the 100 mm pipe (D) is 0.9m/s, calculate the velocity in m/s and the mass flow rate in kg/s in the 170 mm pipe (A.arrow_forwardA 121-mm-diameter pipe enlarges to a 206-mm-diameter pipe. At section 1 of the smaller pipe, the density of a gas in steady flow is 346 kg/m3, and the velocity is 15 m/s; at section 2 of the larger pipe, the velocity is 24 m/s. Find the density in kg/m3 of the gas in section 2.arrow_forward
- The pipe elbow below discharges water at rate of SN/100 (m3/s) into the atmosphere at section 2 (where SN is the sum of your student number). The total volume of the passage between section 1 and 2 is equal to 0.2 m3 and the total mass of the elbow material between section 1 and 2 is equal to 10 x SN (kg). Neglect any friction losses.Calculate the horizontal and vertical forces acting on the elbow. Also calculate the resultant force and angle of force on the elbow. ****SN=21arrow_forward2. Air flows at the rate of 1.5 m²/s through a horizontal pipe with a gradually reducing cross section as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. Take the air density as 1.2 kg/m² and assume inviscid incompressible flow. The change in pressure (P2-P1) (in kPa) between sections 1 and 2 is 200 mm Air Flow 400 mm 1.5 m/s (A) -1.28 (B) 2.56 (C) -2.13 (D) 1.28arrow_forwardQuestion 3 Water enters a U-shape pipe at 50 kg/s mass flow rate at inlet 1 and leaves the U-shape pipe in the angles shown at 40 kg/s and 10 kg/s at outlets 2 and 3, respectively. The total volume of the pipe is 2.2×10-3 m3 and the density of water is 1000 kg/m³. The pressures at points 1, 2 and 3 are 300kPa, 200kPa and 100kPa (atmospheric), respectively. What are the forces needed in the horizontal and vertical directions to hold this pipe in place? 10 kg/s /3 cm 8 45 40 kg/s 10 cm ૭| 50 kg/s 5 cmarrow_forward
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