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Alex is measuring the time-averaged velocity components in a pump using a laser Doppler velocimeter (LDV). Since the laser beams are aligned with the radial and tangential directions of the pum, he measures the urand
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Chapter 9 Solutions
EBK FLUID MECHANICS: FUNDAMENTALS AND A
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- Assume the temperature of the exhaust in an exhaust pipe can be approximated by T = To (1 + ae-bx) [1 + c cos(@t)], where To = 100 °C, a = 3, b = 0.03 m ¹, c = 0.066, and w = 100 rad/s. If the exhaust speed is a constant 3 m/s, determine the time rate of change of temperature of the fluid particles at (a) x = 0 and (b) x = 4 m when t = 0. DT (a) °C/s (b) Dt DT Dt = °C/sarrow_forwardA calibration test of a 2.5cm circular sharp edged orifice in the vertical side of the large tank showed a discharge of 590 N of water collected in 81 seconds, when under a constant head of 4.70 m. In addition, measuremnt of the trajectory of the jet gave the following data: A point on the jet has the coordinates in cm (235, -30), with the orifice located at the origin of the rectangular coordinate system. Find the value of Cc. a.0.629 b.0.98 c.0.989 d.0.636 PLEASE INCLUDE FIGURE OR FBDarrow_forwardA calibration test of a 2.5cm circular sharp edged orifice in the vertical side of the large tank showed a discharge of 590 N of water collected in 81 seconds, when under a constant head of 4.70 m. In addition, measuremnt of the trajectory of the jet gave the following data: A point on the jet has the coordinates in cm (235, -30), with the orifice located at the origin of the rectangular coordinate system. Find the value of Cv. Include FBD. a. 0.629 b. 0.636 C. 0.989 d. 0.98arrow_forward
- Suppose that a fluid has density p (function of space and time) and velocity v with no sources or sinks. (A) Show that the rate of change of the mass m of the fluid contained in a region Q is dm dp -dv. dt (B) Suppose further that, if the fluid crosses the boundary, show that dm - / | (pv) - nds. = - dt (D) Why the continuity equation for water is given by V:(pv) = 0.arrow_forwardThe velocity of the mercury at T_∞=250 o C is U_∞=0.033m/sec, and it flows over the pipe bundle of D= 1.25 cm diameter and L=1.2m length. The ratio of the vertical and diagonal spacing distances for the pipes in the shifted plate arrangement is ST /D=SD /D= 1.405. It consists of a matrix with the number of pipe rows in the horizontal direction NL=60 and the number of pipe rows in the vertical direction NT=30. Pipe wall (surface) temperatures are kept at a uniform temperature of T_w=160 o C. Accordingly, find the average heat transfer coefficient, the total heat transfer coefficient from the mercury to the pipe bundle. (Variables: ST /D=SD /D= 0.75-1.975, U=0.02-0.07m/s, L=0.5-1.4m)arrow_forwardFor the below accelerating flow, we want to find the velocity profile using the integral momentum approximation. Əv, Ət (b) Əy² y U The governing equation for the accelerating flows is given as From the governing equation, show that Н H = 1- P pdfvdy: =-μ dt 3 y 1 y + 28(t) 28(t), Əv d8 When Vx is given as the following equations, show that 8 dt ду ly=0 (1) = 4 (2) for 0≤ y ≤8(t) (3) -=0 for y≥8(t) (8(t): time-dependent boundary layer thicknes) U = (c) Find 8(t) by integrating the equation (2) with respect to t. Then, find the complete Vx by putting 8(t) into the equation (3).arrow_forward
- 5. Find the rate at which a fluid flowing with constant velocity u (3,0,-1) crosses each of the following triangles: (а) [(-2, 1, 0), (5, 3, -1), (8, -5, 2)], (b) [(8, -5, 2), (5, 3,-1), (-2, 1,0)), (c) [(1,-1,0), (2, 0, 2), (3, –2, –3)), (d) [(0,0,0), (0, 1,0), (1,0,0)], (e) [(1,0,0), (0, 1,0), (0,0, 1)], (f) [(0,0,0), (0,0, 1), (0, 1, 0)), (g) [(0,0,0), (1,0, 0), (0,0, 1)].arrow_forwardA B A gas enters a piping section AB from the left at density 1.15 kg/m³ and with speed 4 meters/sec. The pipe section has a constant diameter of 10 centimeters. While passing through AB the gas density changes to 0.95 kg/m³. Determine the speed with which the gas exits section AB in meters/sec. Assume steady flow and use the continuity equation. Your answer should include at least 2 digits after the decimal place.arrow_forward7. For the flow of a thin layer of liquid down an inclined plane shown: a. Using the cross-hatched element and through a force balance, show that the velocity distribution across the layer is: dx Y sin e (b2 – s2) 2 µ и 3 Free Surface an expression for the at the free b. Derive t dx liquid velocity surface. c. Derive an discharge per unit width. d. Derive Fixed y s dx expression for the Wall b an expression for the shear stress at the fixed wall.arrow_forward
- A two-dimensional fluid element of dimensions dx and dy translates and distorts as shown, during the infinitesimal time period dt = t2 − t1. The velocity components at point P at the initial time are u and ? in the x- and y-directions, respectively. Show that the magnitude of the rate of rotation (angular velocity) about point P in the xy-plane isarrow_forwardFor the velocity profile shown find 1.The total displacement ,D(in): 2.The average speed,S(in/s):arrow_forwardA u component of velocity is given by u = Axy, where Ais a constant. What is a possible v component? What must the vcomponent be if the flow is irrotational?arrow_forward
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