A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger

Question

A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger, which is 1.05 cm in diameter. (a) If the hole was 2.00 m below the surface of the North Sea (density 1030 kg/m3), what was the force on his finger? N (b) If he pulled his finger out of the hole, how long would it take the released water to fill 1 acre of land to a depth of 1 ft assuming the hole remained constant in size? (A typical U.S. family of four uses 1 acre-foot of water, 1234 m3, in 1 year.) express the answer in days. please, please show mw all the steps and answer to this problem. thank you.

Explanation / Answer

Pressure = pgh = density * gravity * depth Pressure also equals Force divided by Area So Force = Pressure times Area Force = (density * gravity * depth) * Area Area = (pi/4) d^2 Force = (density * gravity * depth) * (pi/4) d^2 Force = (1030 kg/m^3) * (9.81 m/s^2) * 2m * (pi/4)(0.0105 m)^2 Force = 1.75 N b) the speed of water through the hole would be v = sqrt (2 * g * h) flow rate (Q) = v * A = sqrt (2 * g * h) * (pi/4) d^2 Time to fill = Volume of yard / flow rate Time to fill = Volume of yard / (sqrt (2 * g * h) * ((pi/4) d^2)) Time to fill = 1234 m^3 / (sqrt (2 * (9.81 m/s^2) * 2m) * ((pi/4) (0.0105)^2)) Time to fill = 2276158 sec time to fill = 26.34days

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