A Newtonian fluid flows under steady, laminar conditions through a circular pipe as described in the figure below. Under these conditions, the maximum local velocity (m/s) at a section is most nearly 0.05 m³/s a. 2.0 b. 2.5 C. 6.5 d. 3.0 u(r) = Umax (1-772) D= 14 cm A frictionless, incompressible steady flow field is given by V = 2xyi - y2j in arbitrary units. Let the density be p0 = constant and neglect gravity. Find an expression for the pressure gradient in the y direction. a. μ + poу3 b. - 2μ-2p0y3 c. 2μ + 2p0y ○ d. 2p0y3

A venturi meter, shown in Fig. designed constriction whose pressure difference is a mea- sure of the flow rate in a pipe. Using Bernoulli's equation for steady incompressible flow with no losses, show that the flow rate Q is related to the manometer reading h by is a carefully 2gh(PM – p). A2 VT- (D/D;)4 where py is the density of the manometer fluid. 2

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As shown in the following figure, a pipe of cross-sectional area A = 0.01 m2 and atotal length of 5.5 m is used for siphoning water from a tank. The discharge from the siphonis 1.0 m below the level of the water in the tank. At its highest point, the pipe rises 1.5 mabove the level in the tank.(a) What is the water velocity v (m/s) at the discharge? (b)  What is the lowest gauge pressure (in bars) in the tube?  And wheredoes it occur? Neglect pipe friction. Is the lowest pressure higher than the vapor pressureof water at room temperature?(c) If the siphon reaches virtually all the way to the bottom of the tank (but is notblocked off), is the time taken to drain the tank equal to t = V/Av, where V is the initialvolume of water in the tank, and v is still the velocity (e.g., 4.43 m/s) as computed abovewhen the tank is full? Explain your answer.(d) A siphon can drain the liquid in the tank, which means that the liquid flowsupward at the right-hand side of the tube. It appears to be…

Q.2 The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression R? (dp 1- 4µ ( dx .2 u(r) = %3D R? dp is a constant dx where The average velocity of fluid in the pipe is u(r) R? (dp (b) 4µ ( dx R? (dp (e) - 8µ ( dx R? (dp R? (dp (d) (c) 2µ ( dx, H (dx 응증

For axial flow through a circular tube, the Reynolds numberfor the transition to turbulence is approximately 2300  based on the diameter and average velocity. Ifd= 5 cm and the fl uid is kerosene at 20 ° C, fi nd the volumeflow rate in m 3 /h that causes transition.

The Water is flowing through a pipe having diameter 350 mm and 210 mm at the bottom and upper end respectively. The intensity of pressure at the bottom end is 25.85 N/cm? and pressure at the upper end is 11.6325 N/cm? & the rate of flow through the pipe is 40 lit/s. Draw a neat diagram and determine the following: 1.Velocity head at bottom of the pipe in m/s. 2. Velocity head at top of the pipe in m/s. 3. The difference in datum head between top & bottom in meter of water - 4. The difference of pressure head between bottom to top end in meter of water.- The velocity of flow of water at the bottom in m/s.

Consider steady, incompressible, two-dimensional flow of fluid into a converging duct with straight walls The volume flow rate is V ·, and the velocity is in the radial direction only, with ur a function of r only. Let b be the width into the page. At the inlet into the converging duct (r = R), ur is known; ur = ur(R). Assuming inviscid flow everywhere, generate an expression for ur as a function of r, R, and ur(R) only. Sketch what the velocity profile at radius r would look like if friction were not neglected (i.e., a real flow) at the same volume flow rate.

Find the volume flow rate and direction of a certain fluid flowing in a tube system as shown below. 2 8 10 Flows in cm³/s 1.01 4 in O 2; in O 2; out Cannot be determined; insufficient information. O 1; out

The head-discharge relationship for a certain pump can be represented by the equation H-29-6Q^2 The pump is fixed 2 m shove the water surface tank at a level 10 m above the pump. The suction and delivery pipes are 12 m and 720 m long, respectively and each pipe is 0.5 m in diameter. The Estimate the discharge (in m³/s) at the best operating point for the pumping system,