1).A legendary Dutch boy saved Holland by plugging a hole in a dike with his fin
ID: 1781691 • Letter: 1
Question
1).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 1.00 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.)
2).A 1.02-kg beaker containing 1.95 kg of oil (density = 916.0 kg/m3) rests on a scale. A 1.98-kg block of iron suspended from a spring scale is completely submerged in the oil as shown in the figure below. Determine the equilibrium readings of both scales.
3).In a water pistol, a piston drives water through a larger tube of area A1 into a smaller tube of area A2 as shown in the figure below. The radius of the large tube is 1.10cm and that of the small tube is 1.50 mm. The smaller tube is 3.00 cm above the larger tube.
(a) If the pistol is fired horizontally at a height of 1.40 m, determine the time interval required for water to travel from the nozzle to the ground. Neglect air resistance and assume atmospheric pressure is 1.00 atm.
s
(b) If the desired range of the stream is 7.60 m, with what speed v2 must the stream leave the nozzle?
m/s
(c) At what speed v1 must the plunger be moved to achieve the desired range?
m/s
(d) What is the pressure at the nozzle?
(e) Find the pressure needed in the larger tube.
Pa
(f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.)
N
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) * 1m * (pi/4)(0.0105 m)^2
Force = 0.875 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) * 1m) * ((pi/4) (0.0105)^2))
Time to fill = 3217341.63 sec
time to fill = 37.24 days
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.