Question

A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger, which is 1.20 cm in diameter.

(a) If the hole was 2.80 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.)
days

Answer 1

a) F = PA = ro*g*h*pi*d^2/4

= 1030*9.8*2.80*3.14*.0120^2/4 = 3.196N

b) use Bernoulli equation (neglect viscous losses)

P1/ro/g + v1^2/2/g +z1 = P2/ro/g + v2^2/2/g +z2

pressures cancel (assume both atmospheric)

z1-z2 = 2.80 (assume constant, ie top of water in that acre is below the hole)

assume v1 = 0 (large vessel)

so, we're left with: 2.80 = v2^2/2/g

v2 = sqrt(2.80*2*g) = 7.408 m/s

volumetric flow = v2*A = 0.838e-3 m3/s

time to flood the whole mess = 1234m3/(.838e-3m3/s)

= 1.47 x 10^6 s

= (1.47*10^6)/(60*60*24) days

= 17.05 days