Exam 10: Fluids

Glycerin, with a viscosity of $1.5 \mathrm {~N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 }$ is flowing with an average speed of 1.2 m/s through a tube that has a radius of 5.0 mm and is 25 cm long. What is the drop in pressure over the length of this pipe?

Under standard conditions, the density of air is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ What is the mass of the air inside a room measuring $4.0 \mathrm {~m} \times 3.0 \mathrm {~m} \times 2.0 \mathrm {~m} ?$

A barge is 10 m wide and 60 m long and has vertical sides. The bottom of the boat is 1.2 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } ?$

A piece of aluminum with a mass of 1.0 kg and density of $2700 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ is suspended from a light cord and then completely immersed in a container of water having density 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$ (a) Determine the volume of the piece of aluminum. (b) Determine the tension in the cord when the aluminum is immersed in the container of water.

Ideal incompressible water is flowing in a drainage channel of rectangular cross-section. At one point, the width of the channel is 12 m, the depth of water is 6.0 m, and the speed of the flow is 2.5 m/s. At a point downstream, the width has narrowed to 9.0 m, and the depth of water is 8.0 m. What is the speed of the flow at the second point?

An object has a volume of $4.0 \mathrm {~m} ^ { 3 }$ and weighs 40,000 N. What will its apparent weight be in water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } ?$

A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ How much deeper into the water does the barge sink when $3.0 \times 10 ^ { 5 } \mathrm {~kg}$ of coal are Ioaded on the barge?

A circular window 30 cm in diameter in a submarine can withstand a net maximum force of $5.20 \times$ $10 ^ { 5 } \mathrm {~N}$ without damage. What is the maximum depth in a fresh-water lake to which the submarine can go without damaging the window? The density of fresh water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

If atmospheric pressure increases by an amount $\Delta p$ which of the following statements about the pressure in a lake is true? (There could be more than one correct choice.)

Two horizontal pipes are the same length, but pipe B has twice the diameter of pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe A is $Q = \frac { \Delta V } { \Delta t }$ what is the flow rate in pipe B ?

As shown in the figure, fluid fills a container having several sections. At which of the indicated points is the pressure greatest?

Motor oil, with a viscosity of $0.25 \mathrm {~N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 }$ is flowing through a tube that has a radius of 5.0 mm and is 25 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per second?

A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$ What is its mass?

A 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is $7860 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and that of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A block of metal weighs 40 N in air and 30 N in water. What is the buoyant force on the block due to the water? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

An object floats with half its volume beneath the surface of the water. The weight of the displaced water is 2000 N. What is the weight of the object? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A 12,000-N car is raised using a hydraulic lift, which consists of a $U \text {-tube }$ with arms of unequal areas, filled with oil and capped at both ends with tight-fitting pistons. The wider arm of the $\text { U-tube }$ has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? For purposes of this problem, neglect the weight of the pistons.

A solid sphere of mass 8.6 kg, made of metal whose density is $3400 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ hangs by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 38 N. The density of the liquid is closest to which one of the following values?

A plastic block of dimensions $2.00 \mathrm {~cm} \times 3.00 \mathrm {~cm} \times 4.00 \mathrm {~cm}$ has a mass of 30.0 g. What is its density?

A pressurized cylindrical tank, 5.0 m in diameter, contains water that emerges from the pipe at point C with a speed of 13 m/s as shown in the figure. Point A is 10 m above point B and point C is 3.0 m above point B. The area of the pipe at point B is $0.080 \mathrm {~m} ^ { 2 }$ and the pipe narrows to an area of $0.040 \mathrm {~m} ^ { 2 }$ at point C. Assume that the water is an ideal fluid in laminar flow. The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ The mass flow rate in the pipe is closest to