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Consider the general form of the Reynolds transport theorem (RTT) as stated in Prob. Let B11 be the linear momentum
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FLUID MECHANICS FUNDAMENTALS+APPS
- Q3. The momentum equation for an inviscid flow with body forces ignored is defined as, a(pu) ¸ a(puu) , d(puv) _ _ôP ây + ốt + Show that for incompressible flow in steady-state this simplifies as given below; ди ди + pv- ƏP pu-arrow_forwardFor the flow of a viscous fluid, with the velocity V = f(x)g(y)h(z)i (where f, g, h are arbitrary functions), the following conditions are given: . The flow is adiabatic. • The quantities v = 2 and 3 = $ are constants. • The velocity circulation is conserved for the flow, irrespective of the values of vand 3. What is the general solution for the functions f, g, h?arrow_forwardI am confused whether points A and B do not lie on the same streamline in this equation.arrow_forward
- 9- V(D1)^2=V1(D2)^2 mass 10 points continuity equation O true O False 10-stream line is a line giving 10 points direction of velocity at any point. O True O Falsearrow_forwardPlease explain step by step so I can understandarrow_forwardThe left field wall at a baseball park is 320 feet down the third base line from home plate; the wall itself is 37 feet high. A batted ball must clear the wall to be a home run. Suppose a ball leaves the bat, 3 feet off the ground, at an angle of 45°. Use g = 32 ft/sec as the acceleration due to gravity and ignore any air resistance. Complete parts (a) through (d). (a) Find parametric equations that model the position of the ball as a function of time. Choose the correct answer below. x= (Vo cos 45) t, y = - 16t + (Vo sin 45) t+3 x= (Vo sin 45) t, y = 16t - (Vo cos 45) t+ 3 x= (Vo cos 45) t, y = - 32t + (Vo sin 45)t+3 x= (Vo sin 45) t, y = 32t - (vo cos 45)t+3 (b) What is the maximum height of the ball if it leaves the bat with a speed of 75 miles per hour? Give your answer in feet. The maximum height of the ball is feet. (Type an integer or decimal rounded to two decimal places as needed.) (c) What is the ball's horizontal distance from home plate at its maximum height? Give your…arrow_forward
- The wind flutter on the wing of a newly proposed jet fighter is given by the following 1st order differential equation: dy/dx = 2yx With the Boundary Condition: y(0) = 1 (remember this means that y = 1 when x = 0) Determine the vertical motion (y) in terms of the span (x) of the wing. The frequency of fluctuations of the wing at mach 2 is given by the non-homogenous 2nd order differential equation: y'' + 3y' - 10y = 100x With the boundary conditions: y(0) = 1 and y(1) = 0 (i.e., y = 1 when x = 0 and y = 0 when x = 1) By solving the homogenous form of this equation, complete the analysis and determine the amplitude (y) of vibration of the wing tip at mach 2. Critically evaluate wing flutter and fluctuation frequency amplitude determined by solving the two differential equations above.arrow_forwardOne of the oldest equations in fluid mechanics deals with the flow of a liquid from a large reservoir. Using the Bernoulli equation along the streamline, (a) find out the velocity in m/s at the exit (location (2)) when h = 20 m and (b) find out the velocity in m/s at the location (5) for H = 4 m. Here the gravitational acceleration (g) can be approximated to be 10 m/s². h 147 H d (5) • (1) (3) (2) (4)arrow_forwardFluid Mechanics: Open Channel Flowarrow_forward
- The bernoulli's equation between 2 sections in a flow channel, for ideal fluid is Total Energy available at section1 = Total Energy available at section 2 + Losses OTotal Energy available at section1 Total Energy available at section 2 Total Energy available at section1 = Total Energy available at section 2- Losses Total Energy available at section1 + Total Energy available at section 2 = Lossesarrow_forwardWater with density of 1000 kg/m^3 flows through a horizontal pipe (in the x-z plane) bend as shown. The weight of the pipe is 350 N and the pipe cross-sectional area is constant and equals to 0.35 m^2. The magnitude of the inlet velocity is Section (1) 4 m/s. The absolute pressures at the entrance and exit of the bend are 210 kPa and 110 kPa, respectively. Assuming the atmospheric pressure is 100 kPa and neglecting the weight and viscosity of the water , find the following: Control volume The mass flow rate is 180° pipe bend Section (2) The exit velocity is The force (in the z-axis direction) acting on the fluid isarrow_forwardb) A Newtonian fluid flows in an annular space created by a concentric pipe of radius R, and a rod of radius R;, as shown in Figure Q1(b). The rod is moving at a constant velocity V, while the pipe is stationary. The flow is steady, laminar and incompressible and there is no forced pressure gradient driving the flow. Assuming the velocity components in the radial and tangential directions are zero and ignoring the effects of gravity, derive an expression for the velocity field in the annular space. R. R: Figure Q1(b)arrow_forward
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