Université d’Ottawa Département de génie mécanique University of Ottawa Department of Mechanical Engineering MCG 3340 Fluid Mechanics I Midterm Examination, 5 November 2021 Duration: 80 minutes,...

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Université d’Ottawa Département de génie mécanique University of Ottawa Department of Mechanical Engineering MCG 3340 Fluid Mechanics I Midterm Examination, 5 November 2021 Duration: 80 minutes, Open book, Questions have equal weight Instructor: Dr. Matei Radulescu. Question 1 Water flows steadily through a 90◦ elbow, which is followed by a nozzle, as shown in the sketch below. The elbow is held by a bracket attached to the wall, as shown in the sketch. Upstream of the elbow is a flexible connection which does not transmit any force. If the rate of mass flow of water is 2 kg/s, and the pressure of the water downstream of the connection is 130 kPa absolute, estimate the components of the force applied by the bracket on the wall. The pipe internal diameter D is 5 cm, and the nozzle exit inner diameter d is 2 cm. Take the density of water to be 999 kg/m3. 1 Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Hammad Butter Question 2 The smallest scale in a turbulent flow is η, the size of a Kolmogorov eddy. At smaller scales, viscous effects dissipate the kinetic energy associated with the flow motion. For the turbulent flow generated behind a car moving at 100 km/h, the size of these smallest eddies is approximately η ≈ 2×10−5m. Assuming the air molecules behave like the spherical particles treated in class, estimate how many molecules are contained in a sphere of diameter η. Question 3 Consider a rectangular gate, whose constant width in the direction out of the page is 4L, where L is the distance measured parallel to the gate from the bottom to the fulcrum. If you neglect the gate’s weight, find the height H to which a fluid of density ρ must rise in order to tip over the gate. Express your answer in closed form in terms of L and θ. Hint : recall that (a− b)3 = a3 − 3a2b+ 3ab2 − b3. 2