Water in a container and air in a tornado flow in horizontal circular streamline

Question

Water in a container and air in a tornado flow in horizontal circular streamlines of radius r and speed V at shown in Video V3.6 and Fig. P3.16. Determine the radial pressure gradient, p/ r, needed for the following situations: (a) The fluid is water with r = 3 in. and V =0.8 ft/s. (b) The fluid is air with r = 300 ft and V = 200 mph. FIGURE P3.16 For curved streamlines, - dp / dn = rho V2 / R + r dz / dn, or with dz / dn = 0 (horizontal streamlines), R = r, and d /dn = -d / dr this becomes dp / dr = rho V2 / r With r = 3 / 12 H and V = 0.8 H / 3 and water (p = 1.94 slaps / H3), dp / dr = 1.9 slab / H (0.8 H / 2)2 / 3 / 12 H = 4.97 slogs / H2·s2 = 4.97 16 / H2

Explanation / Answer

to find radial pressure he has taken centrifugal force. i.e. (rho)v^2/r rho is density actually its mv^2/r but the analysis is per unit volume so m/v becomes rho* take an element dn on the wall of the container therefore dp/dn = (rho)v^2/r now dp/dn is also equal to dp/dr as only the radial component is responsible for force on the outer surface and not tangential so dp/dn = dp/dr problem solved then he has just put values

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