Application manometer The liquid in the tube will reach an equilibrium position where its weight will be balanced by the difference between the tank pressure and the local atmospheric pressure exerted on the liquid at D. Thus, Automobile Hydraulic Lift Hydraulic Drum Brake Archimedes principle The principle of buoyancy a submerged body is subject to an upward force FB equal to the weight of the fluid displaced. 3. Fluid Dynamics Laminar flow - fluid moves along smooth paths -viscosity damps any tendency to swirl or mix Turbulent flow -fluid moves in very irregular paths -efficient mixing -velocity at a point fluctuates 3.1 Contro/ Volume Approach Solving problems involving fluids g to pick a fixed region in the fluid and watch the fluid as it enters and leaves the region Conservation laws such as conservation of mass, momentum and energy are applied We don t need to know the flow details within the control volume Example 1 Suppose we are designing a water-piping system for a building with two apartments and wish to supply water to two faucets, which are connected by a tee configuration, as shown in the figure We want the velocity of the water to be same when it leaves both faucets. What should be the velocity of the water source? Analysis 7 Assume that the mass of the fluid per unit time entering the control volume is equal to the amount leaving And assume that the water is steady, not trapped in control volume The density of the water is the same throughout (incompressible fluid), the diameter of the pipe is the same everywhere. Conservation of mass gives the solution 3.2 Fluid Force we assume steady one-dimensional flow, then we may write that the force in the kth direction, Fk, as where is the mass flowrate and(V2k-Vik) is the difference in the velocity of the fluid from station I to station 2 in the kth direction Example 2 Water with a velocity of 10 m/s strikes a turbine used for power generation and is rotated 60" from the horizontal by the blade, as shown in the figure The cross section of the inlet water is 0.003 m2. What is the force on a turbine blade shown in the figure? Solution We may assume incompressible flow, so that p 1=p2, also AI=A2. The water is initially horizontal Applying the idea of conservation of mass indicates that Notice that because A1=A,, then VI=V Applying equation to the x direction yields, Substituting the appropriate numbers into this expression gives The arrow indicates the direction of the x component of the force Likewise, in the y direction, we haveApplication : manometer The liquid in the tube will reach an equilibrium position where its weight will be balanced by the difference between the tank pressure and the local atmospheric pressure exerted on the liquid at D. Thus, Automobile Hydraulic Lift Hydraulic Drum Brake Archimedes’ principle The principle of buoyancy: . A submerged body is subject to an upward force FB equal to the weight of the fluid displaced. 3. Fluid Dynamics Laminar flow — fluid moves along smooth paths — viscosity damps any tendency to swirl or mix Turbulent flow —fluid moves in very irregular paths —efficient mixing —velocity at a point fluctuates 3.1 Control Volume Approach Solving problems involving fluids in motion, ❖ to pick a fixed region in the fluid and watch the fluid as it enters and leaves the region. Conservation laws such as conservation of mass, momentum and energy are applied. We don’t need to know the flow details within the control volume ! Example 1 Suppose we are designing a water-piping system for a building with two apartments and wish to supply water to two faucets, which are connected by a tee configuration, as shown in the figure. We want the velocity of the water to be same when it leaves both faucets. What should be the velocity of the water source? Analysis →Assume that the mass of the fluid per unit time entering the control volume is equal to the amount leaving. And assume that the water is steady, not trapped in control volume. . → The density of the water is the same throughout (incompressible fluid) , the diameter of the pipe is the same everywhere. Conservation of mass gives the solution. . 3.2 Fluid Force we assume steady one-dimensional flow, then we may write that the force in the kth direction, Fk , as : where is the mass flowrate and (V2k－V1k) is the difference in the velocity of the fluid from station 1 to station 2 in the kth direction. Example 2 Water with a velocity of 10 m/s strikes a turbine used for power generation and is rotated 60˚ from the horizontal by the blade, as shown in the figure. The cross section of the inlet water is 0.003 m2. What is the force on a turbine blade shown in the figure? Solution We may assume incompressible flow, so that ρ1=ρ2 , also A1=A2 . The water is initially horizontal means that v1y=0. Applying the idea of conservation of mass indicates that : Notice that because A1 = A2 , then V1 = V2 . Applying equation to the x direction yields, Substituting the appropriate numbers into this expression gives: The arrow indicates the direction of the x component of the force. Likewise, in the y direction, we have