A cylindrical-shaped pipe can carry water from a very largeelevated container on the left to a lowe container on the right.The area of the wider portion of the pipe containing the point bhas a cross sectional area Ab=7.80 x 10^-3 m^2, and the narrowersection of the pipe containing both points c and d has a crosssectional area of Ac= 3.14 x 10^-4 m^2. Point C is at height ofy2=2m above point d. A water valve closes the elevated container atpoint a, and thus there is initially only water in the uppercontainer, and none in the pipe. The rectangular block in the lowercontainer above has dimensions 10 cm x 3cm x 3cm and mass 0.075 kg,and it rests on the bottom of the lower container before any waterenters the lower container.
a) If the pressure at the surface of the water is 1 atm, what isthe absolute pressure at point a which is at a depth of y1=2 metersbelow the surface of the water in the tank?
The valve at point a is opened to create an opening equal to thearea of the pipe containing the point b so that water flows formthe elevated container through the pipe, and into the lowercontainer.
b) Consider the pressure at pints b and c. At which of these pointsis the pressure least? Justify your answer.
c) If the speed of the water at point b is vb=6 m/s, what is thespeed of the water at point c?
d) Determine vd, the speed at which the water initially enters thelower container.
e) As the water level rises in the lower container, the blockeventually begins to float. What is the height h of the water levelat the instant the block is lifted off the bottom of the container,that is, the block just begins to float?
A cylindrical-shaped pipe can carry water from a very largeelevated container on the left to a lowe container on the right.The area of the wider portion of the pipe containing the point bhas a cross sectional area Ab=7.80 x 10^-3 m^2, and the narrowersection of the pipe containing both points c and d has a crosssectional area of Ac= 3.14 x 10^-4 m^2. Point C is at height ofy2=2m above point d. A water valve closes the elevated container atpoint a, and thus there is initially only water in the uppercontainer, and none in the pipe. The rectangular block in the lowercontainer above has dimensions 10 cm x 3cm x 3cm and mass 0.075 kg,and it rests on the bottom of the lower container before any waterenters the lower container.
a) If the pressure at the surface of the water is 1 atm, what isthe absolute pressure at point a which is at a depth of y1=2 metersbelow the surface of the water in the tank?
The valve at point a is opened to create an opening equal to thearea of the pipe containing the point b so that water flows formthe elevated container through the pipe, and into the lowercontainer.
b) Consider the pressure at pints b and c. At which of these pointsis the pressure least? Justify your answer.
c) If the speed of the water at point b is vb=6 m/s, what is thespeed of the water at point c?
d) Determine vd, the speed at which the water initially enters thelower container.
e) As the water level rises in the lower container, the blockeventually begins to float. What is the height h of the water levelat the instant the block is lifted off the bottom of the container,that is, the block just begins to float?
