Each of five cylindrical drums with radius R is filled to a height h above the bottom with a liquid of density p. Rank the drums in order of the pressure at the bottom of the drum, largest to smallest. (a) R=40 cm, h=80 cm, p=1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (b) R=40 cm, h=100 cm, p=1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (c) R=50 cm, h=100 cm, p=800 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (d) R=50 cm, h=80 cm, p=800 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (e) R=50 cm, h=125 cm, p=800 $\mathrm { kg } / \mathrm { m } ^ { 3 }$.

A section of pipe with an internal diameter of 10.0 cm tapers to an inner diameter of 6.00 cm as it rises through a height of 1.70 m at an angle of

$$60.0 ^ { \circ }$$

with respect to the horizontal. The pipe carries water and its higher end is open to air. (a) If the speed of the water at the lower point is 15.0 cm/s, what are the pressure at the lower end and the speed of the water as it exits the pipe? (b) If the higher end of the pipe is 0.300 m above ground, at what horizontal distance from the pipe outlet does the water land?

A cube that is 4.00 cm on a side and of density

$$8.00 \times 10 ^ { 2 } \mathrm { kg } / \mathrm { m } ^ { 3 }$$

is attached to one end of a spring. The other end of the spring is attached to the base of a beaker. When the beaker is filled with water until the entire cube is submerged, the spring is stretched by 1.00 cm. What is the spring constant?

The potential energy associated with surface tension is much like the elastic potential energy of a stretched spring or a balloon. Suppose we do work on a puddle of liquid, spreading it out through a distance of

$$\Delta s$$

along a line L perpendicular to the force. (a) What is the work done on the fluid surface in terms of

$$\gamma , L$$

, and

$$\Delta s ?$$

(b) The work done is equal to the increase in surface energy of the fluid. Show that the increase in energy is proportional to the increase in area. (c) Show that we can think of

$$\gamma$$

as the surface energy per unit area. (d) Show that the SI units of surface tension can be expressed either as N/m (force per unit length) or

$$J/m^2$$

(energy per unit area).

A dinoflagellate takes 5.0 s to travel 1.0 mm. Approximate a dinoflagellate as a sphere of radius 35.0

$$\mu \mathrm { m }$$

(ignoring the flagellum). (a) What is the drag force on the dinoflagellate in seawater of viscosity 0.0010

$$\mathrm { Pa } \cdot \mathbf { s } ?$$

(b) What is the power output of the flagellate?

A hydraulic lift is lifting a car that weighs 12 kN. The area of the piston supporting the car is A, the area of the other piston is a, and the ratio A/a is 100.0. How far must the small piston be pushed down to raise the car a distance of 1.0 cm? [Hint: Consider the work to be done.]