Find the shear and normal stresses on plane AA cutting through at 30°. Solution: Make cut “AA” so that it just hits the bottom right corner of the element. This gives the freebody shown at right. Now sum forces normal and tangential to side AA. Denote side length AA as “L.” | Chapter 2 Pressure Distribution in a Fluid For the two-dimensional stress field in Fig. let cxx 3000 psf cyy 2000 psf xy 500 psf Find the shear and normal stresses on plane AA cutting through at 30 . Solution Make cut AA so that it just hits the bottom right corner of the element. This gives the freebody shown at right. Now sum forces normal and tangential to side AA. Denote side length AA as L. Fn AA 0 CAAL - 3000sin30 500cos30 Lsin30 - 2000 cos30 500sin 30 L cos30 Solve for cAA 2683 lbf ft2 Ans. a Fig. Ft AA 0 taaL - 3000 cos30 - 500 sin30 L sin30 - 500 cos30 - 2000 sin30 L cos30 Solve for taa 683 lbf ft2 Ans. b For the stress field of Fig. change the known data to cxx 2000 psf cy 3000 psf and cn AA 2500 psf. Compute cxy and the shear stress on plane AA. Solution Sum forces normal to and tangential to AA in the element freebody above with cn AA known and cx unknown EFn AA 2500L - cxy cos30 2000 sin30 L sin30 - cxy sin 30 3000 cos 30 Lcos30 0 Solve for cxy 2500 - 500 -2250 - -289 lbf ft2 Ans. a 62 Solutions Manual Fluid Mechanics Fifth Edition In like manner solve for the shear stress on plane AA using our result for 7xy EFt AA taaL - 2000cos30 289sin30o Lsin30 289 cos30 3000 sin30 L cos30 0 Solve for taa 938 -1515 --577 lbf ft2 Ans. b This problem and Prob. can also be solved using Mohr s circle. A vertical clean glass piezometer tube has an inside diameter of 1 mm. When a pressure is applied water at 20 C rises into the tube to a height of 25 cm. After correcting for surface tension estimate the applied pressure in Pa. Solution For water let Y N m contact angle 0 0 and y 9790 N m3. The capillary rise in the tube from Example of the text is 2 N m cos 0 m ca yR 9790 N m3 m Then the rise due to applied pressure is less by that amount hpress m - m m. The applied pressure is estimated to be p Yzpress 9790 N m3 m - 2160 Pa Ans. Given a flow pattern with isobars po - Bz Cx2 .
