1. Two water jets of equal size and speed strike each other as shown in figure. Determine the speed, V, and direction, θ, of the resulting combined jet. Gravity is negligible. Linear momentum equation along the x-direction for the control volume shown above: Linear momentum equation along the y-direction for the control volume shown above: Conservation of mass: From Eqs. (1) and (2): [ ] Combining Eqs. (2) and (3): [( ) ] V = 3 m/s 0.03 m 0.03 m (1) (2) (3) https://www.coursehero.com/file/7363601/Practice-Midterm-II-Solutions/This study resource wasshared via CourseHero.com2. The pump shown in figure adds 20 kW of power to the flowing water. The only loss is that which occurs across the filter at the inlet of the pump. Determine the head loss for this filter. where z1 = z2, P1 = 20 kPa, P2 = 0, and = 6.37 m/s, = 25.5 m/s Also, ( ) = 40.8 m Thus Eq. (1) becomes: https://www.coursehero.com/file/7363601/Practice-Midterm-II-Solutions/This study resource wasshared via CourseHero.com3. The velocity potential for a certain inviscid flow field is : where Φ has the unit of m2/s when x and y are in meters. Please determine the pressure difference in kPa between the points (0.3, 0.6) and (1.2, 1.2), where the coordinates are in meters. Please note that the fluid is water and the elevation changes are negligible. Since the flow is irrotational: At x = 0.3 m and y = 0.6 m so that: and . At x = 1.2 m and y = 1.2 m : So that . Thus, from Eq. (1) : ( ) (1) https://www.coursehero.com/file/7363601/Practice-Midterm-II-Solutions/This study resource wasshared via CourseHero.com4. A thin layer of an incompressible fluid flows steadily over a horizontal smooth plate as shown in figure. The fluid surface is open to the atmosphere, and an obstruction having a square cross section is placed on the plate as shown. A model with a length scale of ¼ and a fluid density scale of 1.0 is to be designed to predict the depth of fluid, y, along the plate. Assume that inertial, gravitational, surface tension, and viscous effects are all important. What are the required viscosity and surface tension scales? A fluid dynamics problem for which inertial, gravitational, surface tension, and viscous effects are all important requires Froude, Reynolds, and Weber number similarity. √ √ Froude number similarity with g = gm follows that: √ For Reynolds number similarity: So that: √ ( ) ( ) V d h Free surface y https://www.coursehero.com/file/7363601/Practice-Midterm-II-Solutions/This study resource wasshared via CourseHero.comFor Weber number similarity: Hence: (√ ) ( ) https://www.coursehero.com/file/7363601/Practice-Midterm-II-Solutions/This study resource wasshared via CourseHero.comPowered by TCPDF
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