Fluidos Ii

Problems

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Define pl, = p + y h as the kinetic pressure and C write Eq. 7.3.5 or 7.3.1 1 in terms o y,. Can we let dp,ldx = ApA/L,where L is the length over which ApL is measured? If so, express u(r) in terms of Apk/L. Verify that Eq. 7.3.13 is, in fact, correct. A parabolic profile is measured in a pipe flow. The flow is: I. Laminar A. I and 111 11. Developed B. I, 11, and 111III. Steady C. I, 11, and IV D. I, 11, IV, and IV IV. Symmetric A pressure drop of 0.07 psi occurs over a section of 0.8-in.-diameter pipe transporting water at 70°F. Determine the length of the horizontal section if the Reynolds number is 1600. Also, find the shear stress at the wall and the friction factor. Find the angle 0 of the 10-mm-diameter pipe of Fig. P7.19 in which water at 40°C isflowing with R e = 1500 such that no pressure drop occurs. Also, find the flow rate.

7.23

maximum allowable diameter? What is the pressure drop over 30 ft of horizontal pipe for this diameter'? Estimate the flow rate through the smooth pipe shown in Fig. P7.23. How long is the entrance region? Assume a laminar flow.

FIGURE P7.23 7.24 A manufacturer of small-diameter tubes wishes to know if thediameters are, in fact, accurate. An experimental setup, like that in Fig. P7.23, is used with a 4-m-long horizontal tube transporting 20°C water with a head of 4 m. If 3.4 L of water is collected in 60 min, what is the inside diameter of the tube, neglecting the effect of the entrance region? Is the effect of entrance region actually negligible? Air at 70°F flows in a horizontal 0.8-in.-diameterpipe. Calculate the maximum pressure drop in a 30-ft section for a laminar flow. Assume that p = 0.0024 slug/ft3. Water at 20°C flows in the 4-mm-diameter pipe of Fig. P7.26. The pressure rise over the 10-m section is 6 kPa. Find the Reynolds number of the flow and the wall shear stress. Assume laminar flow.

7.25

7.26 FIGURE P7.19
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A liquid is pumped through a 2-cm-diameterpipe at a flow rate of 12 Llmin. Calculate the pressure drop in a 10-m horizontal section if the liquid is: (a) SAE-1OW oil at 20°C (b) Water at 20°C (c) Glycerine at 40°C Is the assumption of laminar flow acceptable? A liquid flows with no pressure drop in a vertical 2-cm-diameter pipe. Find the flow rate if, assuming a laminar flow. the liquid is: (a) Water at 5°C (b) SAE-30W oil at 25°C (c)Glycerine at 20°C Is the assumption of laminar flow acceptable? A laminar flow is to exist in a pipe transporting 0.12 ft3/sec of SAE-10W oil at 70°F. What is the

FIGURE P7.26 A research experiment requires a laminar flow of air at 20°C through a 10-cm-diameter pipe at a Reynolds number of 40 000. What maximum velocity is to be expected? What would be the pressure drop over a 10-m horizontal lengthof developed flow? How long would the entrance region be'? Use p = 1.2 kg/m3.

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Chapter 7 / Internal Flows

Calculate the radius where a pitot probe must be placed in the laminar liquid flow of Fig. P7.28 so that the flow rate is given by

T-R'WH.

Water at 20°C flows between the two c o m e horizontal pipes o l Fig. P7.33 with diameter 2 cm and 3 cm A p r a m r e drop of 100 Pa Irme sured over a 10-m section oi developed l a m ~ ~ i d r flow. Find the flow rate and the shear stress o n t ~ n n e pipe. r

FIGURE P7.28 A laminar flow of water at 20°C occurs In a vertical 2-mm-diameter pipe. Calculate the flow rate if the pressure is constant. Is it reasonable to assume a laminar flow? Find the radius in a developed laminar flow in a pipe where: (a) The velocity is equalto the average velocity. (b) The shear stress is equal to one-half the wall shear stress. Find the ratio of the total flow rate through a pipe of radius ro to the flow rate through an annulus with inner and outer radii of ro/2 and ro. Assume developed laminar flow with the same pressure gradient. A laminar flow of water at 60°F is obtained in a research lab at R e = 20,000 in a horizontal...