CEE 341 Fluid Mechanics for Civil Engineers Homework #5 Problem 1: A circular pipe with radius ro is connected to a tank. When water starts flowing in the pipe, the velocity profile changes from uniform (at section 1: u₁) to parabolic (at section 2: Иг = 2u₁ [1-(+)²)) because of wall shear stress To. Assuming a constant To between sections 1 and 2 (distance between the sections L = 2 m), find the value of to knowing that ro = 0.2 m, u₁ = 3 m/s, and the pressures are p₁ = 230 kPa and p2 = 200 kPa. Assume density p = 997 kg/m³. Το x Problem 2: As shown in the figure below, water is pushed steadily by a piston and exits out of a nozzle that converges from diameter D to d. The nozzle does not move because a support is applied and, because of that, the support experiences a force F2. Neglecting the (i) cumulative momentum change between the piston and the nozzle, and (ii) the friction between the piston and the walls: (a) Determine which force between F₁ or F2 is larger without performing any computation. Justify your answer. (b) If Vpiston = 0.6 m/s, D = values of F₁ and F₂? 100 mm, d = 20 mm and density of water 1000 kg/m³, what are the | Vpiston F2 D Jet 1 Problem 3: A vane moves horizontally at a constant velocity V₁ = 4 m/s to the right and deflects a water jet that arrives at a speed V₁ = 17 m/s. The water jet has a diameter d = 10 cm. What are the forces in the x and y directions experienced by the vane? Neglect friction (Note that, since the vane moves horizontally, the figure shows a planar view). V₁ ✓ 45° x Problem 4: Water flows in a pipe at a rate Q = 1 m³/s and is discharged in the atmosphere through a double horizontal nozzle, as shown below. The velocity at cross sections A and B are the same. The pipe diameter is Dpipe 35 cm, while the nozzle diameters are D₁ = 13 cm and DB = 15 cm. Find the force in the x-y plane acting on the flange bolts required to hold the nozzle in place. Note that, since the nozzle is horizontal, the figure shows a planar view). = A 30° B x 2