shows a large reservoir of water connected to a smaller chamber that is sealed b
ID: 1815814 • Letter: S
Question
shows a large reservoir of water connected to a smaller chamber that is sealed by a light (hence ignore its weight) frictionless piston of cross - sectional area 0.01 m2 that supports a load of mass m. (Take water density to be 1000 kg/m3 and gravitational acceleration as 10 m/s2). Determine the value of the water pressure acting on the piston. Find the mass, m, of the load supported. Sufficient water is now added to the large reservoir so that the load (and piston) moves up by a distance of 10 cm. By how much docs the water level in the main tank rise to achieve this. Explain the reasoning for your answer. The change that occurred in Part (iii) means that the load has gained additional potential energy; what was the source of this energy?Explanation / Answer
a) water pressure acting on the piston P = Patm + gh
= Patm + 1000 kg/m3*10 m/s2*(0.6-0.4)m
= 101325 N/m2 + 2000 N/m2 = 103325N/m2, in perpendicular upward direction
b) there is also atmospheric pressure acting on the piston inperpendicular downward direction
so, net pressure in upward direction = 2000 N/m2
so, net pressure force in upward direction = 2000 N/m2 *0.01m2 = 20N
As the piston is in equilibrium this force will be equal andopposite to weight of the load
or, 20N = mg
or, m = 20N/(10m/s2) = 2kg
c) As the system is in equilibrium i.e. pressure force is balancedby weight of the load
always at the piston there should be a hydrostatic pressure ofPatm+ 2000 N/m2
or, gauge pressure of 2000 N/m2
or, height from the zero gauge pressure level(from the main tank) =(2000N/m2)/g =(2000N/m2)/(1000kg/m3*10m/s2)
= 0.2 m = 20cm
Now as load and piston moves up by 10 cm, water in the maintank will also move up by 10 cm to keep the height of thepiston at 20 cm.
d) Suppose after adding water in the main tank, load would not havemoved up. The pressure at the piston will increase and this willgive fluid a flow energy (flow energy = P/). Thusthis flow energy will move the fluid up and doing so pressure will decrease and thus the flow energy will decrease,Which gets accumulated as load's potential energy.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.