Exam 10: Fluids

Water is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of water is 8.0 m, and the speed of the flow is 2.5 m/s. What is the mass flow rate of the water? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A 100-kg person sits on a 5-kg bicycle. The total weight is borne equally by the two wheels of the bicycle. The tires are 2.0 cm wide and are inflated to a gauge pressure of $8.0 \times 10 ^ { 5 } \mathrm {~Pa}$ What length of each tire is in contact with the ground?

A container has a vertical tube, whose inner radius is 20.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube -level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C , whose density is $900 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ The density of the unknown liquid is closest to

A 4.7-kg solid sphere, made of metal whose density is $4000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ hangs by a light cord. When the sphere is immersed in water, what is the tension in the cord? The density of water is 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 } \text {. }$

A hot air balloon along with its cargo has a mass of $4.0 \times 10 ^ { 5 } \mathrm {~kg}$ and it holds $7.0 \times 10 ^ { 5 } \mathrm {~m} ^ { 3 }$ of hot air. It is floating at a constant height in air with a density of $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ What is the density of the hot air in the balloon?

An incompressible ideal fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s . What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

If a ship has a mass of 10 million kilograms, what volume of fresh water must it displace in order to float? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Water, which we can treat as ideal and incompressible, flows at 12 m/s in a horizontal pipe with a pressure of $3.0 \times 10 ^ { 4 } \mathrm {~Pa}$ If the pipe widens to twice its original radius, what is the pressure in the wider section?

A 13,000-N vehicle is to be lifted by a 25-cm diameter hydraulic piston. What force needs to be applied to a 5.0 cm diameter piston to accomplish this? Assume the pistons each have negligible weight.

Consider a very small hole in the bottom of a tank that is 17.0 cm in diameter and filled with water to a height of 90.0 cm. Find the speed at which the water exits the tank through the hole.

As shown in the figure, a large open tank contains a layer of oil $\text { (density } 450 \mathrm {~kg} / \mathrm { m } ^ { 3 } \text { ) }$ floating on top of a layer of water $\text { (density } \left. 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \right)$ that is 3.0 m thick, as shown in the sketch. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be $8.5 \times 10 ^ { 4 } \mathrm {~Pa} ?$

For a certain patient, the build-up of fatty tissue on the wall of an artery has decreased the arterial radius by 10%. By how much would the pressure provided by the heart have to be increased to maintain a constant volume of blood flow? Model the blood as an ideal incompressible fluid.

Water flows out of a large reservoir through 5.0-cm diameter pipe. The pipe connects to a 3.0-cm diameter pipe that is open to the atmosphere, as shown in the figure. What is the speed of the water in the 5.0-cm pipe? Treat the water as an ideal incompressible fluid.

When a container of water is placed on a laboratory scale, the scale reads 120 g. Now a 20-g piece of copper $\text { (of density } 8.9 \mathrm {~g} / \mathrm { cm } ^ { 3 } \text { ) }$ is suspended from a thread and lowered into the water, not touching the bottom of the container. What will the scale now read? The density of water is 1.0 $\mathrm { g } / \mathrm { cm } ^ { 3 }$

Substance A has a density of 3 g/cm³ and substance Bhas a density of 4 g/cm³. In order to obtain equal masses of these two substances, what must be the ratio of the volume of A to the volume of

A solid object floats in water with three-fourths of its volume beneath the surface. What is the object's density? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Ideal incompressible water flows through a horizontal pipe of cross-sectional area $10.0 \mathrm {~cm} ^ { 2 }$ at a pressure of 0.250 atm with a volume flow rate of $1.00 \times 10 ^ { - 3 } \mathrm {~m} ^ { 3 } / \mathrm { s }$ At a valve, the effective cross-sectional area of the pipe is reduced to $5.00 \mathrm {~cm} ^ { 2 }$ What is the pressure at the valve?

A 1938 nickel has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density?

A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the absolute (total) pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?

A brick weighs 50.0 N, and measures $30.0 \mathrm {~cm} \times 10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm}$ What is the maximum pressure it can exert on a horizontal surface due to its weight?