# Force and Flooding Problems

The story goes that a boy in Holland saved his country from being flooded by plugging a hole in the sea wall with his finger. Parts of Holland are lower than sea level and walls have been built to keep the sea out. If the hole was 2.00m below sea level and the density of the North Sea is 1030 kg/m3.

a) What was the force on his finger (diameter 1.20cm)?

b) How long would it take to flood 1 acre of land to a depth of 1 foot if he pulled his finger out? Assume the hole did not get any bigger which is probably not a very realistic assumption.

c) Find a water bill and work out how much water you use in a year and compare this to the amount of water in a foot-acre.

https://brainmass.com/physics/work/force-flooding-problems-477179

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Please see the attachment for the complete solutions.

The story goes that a boy in Holland saved his country from being flooded by plugging a hole in the sea wall with his finger. Parts of Holland are lower than sea level and walls have been built to keep the sea out. If the hole was 2.00m below sea level and the density of the North Sea is 1030 kg/m3

a) what was the force on his finger (diameter 1.20cm)?

b) how long would it take to flood 1 acre of land to a depth of 1 foot if he pulled his finger out? Assume the hole did not get any bigger which is probably not a very realistic assumption.

c) find a water bill and work out how much water you use in a year and compare this to the amount of water in a foot-acre.

Solution:

(Please see the attached file).

a) Sea water pressure at a depth of 2 m = P = Height of water column x Density of sea water x acceleration due to gravity = 2 x 1030 x 9.8 = 20188 Pa

Diameter of the hole d = 1.2 cm or 0.012 m

Area of the hole = Πd2/4 = 3.14 x 0.0122/4 = 1.13 x 10-4 m2

Force acting on boy's finger = Pressure at the hole x Area = 20188x1.13x10-4=2.28 N

b) To determine the time taken to fill a certain volume of space we must first determine the rate at which water escapes from the hole. To do so we apply Bernoulli's equation to two points viz. point 1 at the top of the sea surface and point 2 just outside the hole.

Bernoulli's equation: P + ρgh + ½ ρv2 = Constant .......(1)

Where P = Pressure, ρ = Density of water, v = Speed of water, h = Height above a defined reference.

At point 1: Pressure P1 = Atmospheric pressure, ρ = 1030 kg/m3, Height above the hole h1 = 2 m, Speed at which sea water level goes down = 0.

At point 2: Pressure P2 = Atmospheric pressure, ρ = 1030 kg/m3, Height above the hole h2 = 0, Speed at which water escapes from the hole = v2

Applied to the two points equation (1) can be written as:

P1 + ρgh1 + ½ ρv12 = P2 + ρgh2 + ½ ρv22

Substituting values:

Patm + 1030x9.8x2 + ½ x1030x0 = Patm + 1030x9.8x0 + ½ x1030xv22

1030x9.8x2 = ½ x1030xv22

v2 = 6.26 m/s

Rate of flow of water from the hole Q = Speed x Area of the hole = 6.26x1.13x10-4

=> Q = 7.07 x 10-4 m3/sec

Next we determine total volume of flooded water.

Area of the land A = 1 acre = 4046.86 m²

Depth = 1 foot = 0.3 m

Total volume of flooded water = 4046.86 x 0.3 = 1214 m3

Time taken to fill this much water = Volume/Rate of flow =

1214/7.07x10-4 = 171.7x104 sec = 171.7x104/3600 = 477 hours

c) Average water consumption per person per day in USA = 370 Litres

(Ref: http://en.wikipedia.org/wiki/Water_supply_and_sanitation_in_the_United_States )

Average water consumption per person per year = 370 x 365 = 135050 Litre

As 1 Litre = 0.001 m3, this is equal to 135 m3.

Hence, amount of water in an acre foot is equal to 1214/135 = 9 times the average water consumption per person per year.

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