Near Neverland Ranch, there is a big beautifulpink dam. First thing in the morni

Question

Near Neverland Ranch, there is a big beautifulpink dam. First thing in the morning of everyday, Michael Jacksonopens his window and gazes at this big beautiful pink dam. And heexclaims, “Hurray for pink, my favorite color!!”.Unfortunately, one day, a leak forms in the big beautiful pink dam.That is, water flows through a hole of 1 cm in diameter. Thevelocity of the water exiting the hole is 30 m/s. (Make sure toinclude the effects of atmospheric pressure.) *please helpMichael!* : )

If you plug the leak by covering the hole withyour thumb, what is the force that water applies to yourthumb?

Explanation / Answer

Speed v = 30 m / s diameter d= 1 cm = 0.01 m (a). The height of the water above the hole h = v^2 / (2g )                                                                     =45.91 m (b). Pressure at point A is P = P ' + ( 1/ 2) v ^2 where = density of water = 1000 kg / m^3           P ' =density at top of the dam = 1 atm = 101.3 * 10 ^ 3 Pa So, P = (101.3*10^3 ) + ( 1054.24*10^3 )          =1155.54*10^3 Pa

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