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# Week 1 review MEE 640

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## Popular in Advanced fluid mechanics

## Popular in Mechanical Engineering

This 38 page Class Notes was uploaded by Kartheek Notetaker on Tuesday August 23, 2016. The Class Notes belongs to MEE 640 at Northern Illinois University taught by Dr. Cho in Fall 2016. Since its upload, it has received 8 views. For similar materials see Advanced fluid mechanics in Mechanical Engineering at Northern Illinois University.

## Popular in Mechanical Engineering

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Date Created: 08/23/16

Review of fluid mechanics Example problems Hydrostatic Pressure: example problem Hydrostatic Pressure: example problem Two chambers with the same fluid at their base are separated by a 30-cm-diameter piston whose weight is 25N. Calculate the gage pressures in chambers A and B. Hydrostatic Pressure: example problem Consider a hydraulic jack being used in a car repair shop. The pistons have an area of A = 0.8 cm and A = 0.04 m . Hydraulic oil with a specific gravity of 0.870 is pumped 1 2 in as the small piston on the left side is pushed up and down, slowly raising the larger piston on the right side. A car that weighs 13,000 N is to be jacked up. (a) At the beginning, when both pistons are at the same elevation (h = 0), calculate the force 1 in newtons required to hold the weight of the car. (b) Repeat the calculation after the car has been lifted two meters (h = 2 m). Hydrostatic Pressure: example problem The water tank having 3 m wide into paper is pressurized, as shown by the mercury- manometer reading. Neglecting atmospheric pressure, a) what is the pressure at ? Calculate b) horizontal force, c) vertical force, and d) resultant force on quarter-circle panel. Densities of water and mercury are 1,000 kg/m and 13,600 kg/m , respectively. Buoyancy The density of a liquid is to be determined by an old 1-cm-diameter cylindrical hydrometer whose division marks are completely wiped out. The hydrometer is first dropped in water, and the water level is marked. The hydrometer is then dropped into the other liquid, and it is observed that the mark for water has risen 0.3 cm above the liquid–air inter- face. If the height of the original water mark is 12.3 cm, determine the density of the liquid. (Hint, the hydrometer is in static equilibrium) Example problem 1) Calculate the material acceleration at the point (x = 2m, y = 3m) 2) Acceleration vecറor, ???? Example problem Incompressible steady flow in the inlet between parallel plates is uniform, u = U = 8 cm0s, while downstream the flow develops into the parabolic laminar profile, ???? = ????????(???? − ????), 0 where a is a constant. If z0= 4 cm and the fluid is SAE 30 oil at 20°C, what is the value of u max in cm/s? (Hint: use mass conservation equation) Example problem Example problem Example problem A horizontal water jet of constant velocity V impinges normally on a vertical flat plate and splashes off the sides in the vertical plane. The plate is moving toward the oncoming water jet with velocity ½V. If a force F is required to maintain the plate stationary, how much force is required to move the plate stationary, how much force is required to move the plate toward the water jet? Example problem A sluice gate, which controls flow rate in a channel by simply raising or lowering a vertical plate, is commonly used in irrigation systems. A force is exerted on the gate due to the difference between the water heights y an1 y and 2he flow velocities V and V1upstre2m and downstream from the gate, respectively. Take the width of the sluice gate (into the page) to be w. Wall shear stresses along the channel walls may be ignored, and for simplicity, we assume steady, uniform flow at locations 1 and 2. Neglect momentum correction factor. Develop a relationship for the force F Rcting on the sluice gate as a function of depths y 1 and y , velocity V and V , gravitational constant g, gate width w, and water density, . 2 1 2 Example problem 3 Water flows steadily through a splitter as shown in Figure with ∀ = 0.08 m 1s, ∀ = 0.05 2 m /s, D 1 D = 22 cm, D = 10 c3. If the pressure readings at the inlet and outlets of the splitter are P 1 100 kPa, P = 92 kPa and P = 80 kP3, determine external force needed to hold the device fixed. Disregard the weight effects and momentum correction factor. Density of water is 1000 kg/m . 3 (Hint: pressure always acts on the object in normal and inward direction, and watch “the sign”; check the direction of pressure and velocity with respect to reference coordinate) Example problem A fluid is flowing through a pipe, and the flow is laminar (i.e. Re < 2300) and fully developed. Velocity profile, average velocity, and volumetric flow rate of the pipe flow need to be specified. (Hint: apply momentum balance on the differential control volume) 1) What are the boundary conditions to be used to get the particular solution of velocity from general solution? 2) Obtain velocity profile. 3) Obtain average velocity and its relation with maximum velocity 4) Obtain volumetric flow rate Moody Chart 2300 4000 * Empirical equations Cole brook equation Implicit in f (f appears on both sides): iteration Haaland equation Table 8-4 Rounding of an inlet makes a big difference Rounding of an outlet makes no difference Table 8-4 ???? ???? ????????,???????????????????? ???????????????? Large velocity is used by convention in the equation for minor head loss Table 8-4 For Tees, there are two values of K , one for branch L flow and one for line flow Example problem Example problem Example problem Problem 5 Water at 15°C is to be discharged from a reservoir at a rate of 18 L/s using two horizontal cast iron pipes connected in series and a pump between them. The first pipe is 20 m long and has a 6-cm diameter, while the second pipe is 35 m long and has a 4-cm diameter. The water level in the reservoir is 30 m above the centerline of the pipe. The pipe entrance is sharp-edged, and losses associated with the connection of the pump are negligible. Neglecting the effect of the kinetic energy correction factor, determine the required pumping head and the minimum pumping power to maintain the indicated flow rate. Summary of equations Cartesian coordinates (x, y, z) and (u, v, w) Summary of equations Cylindrical coordinates (r, , z) anr (, z , u ) Example problem Example problem Modification Example problem Modification V Example problem Modification Example problem Example problem Example problem Example problem Example problem

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