Fluids

A small and uniform 10. $0kg$ object floats at rest with 75% of the object submerged in a cubical tank containing 50.0 $m^{3}$ of water. What is the buoyant force acting on the object? Treat $g=10^{m}/s^{2}$

(A) 500000 $N$
(B) 375000 $N$
(C) 100 $N$
(D) 75 $N$
(E) 25 $N$

An open cylindrical container with very large radius is at rest a distance $H$ above the ground at the edge of a platform. A tiny hole develops at the bottom of the container and water from the container squirts out horizontally landing a distance $H$ from the edge of the platform. For the water to land at this location, what is the depth of the water $L$ in the container? The figure is not drawn to scale and air resistance is ignored.

(A) $H/4$ (B) $H/\sqrt{2}$ (C) $H$ (D) $H\sqrt{2}$ (E) $2H$

The density of a solid cubic block is given as $\rho=0.750g/_{cm^{3}}$. This block is dropped into a large swimming pool filled with water. When equilibrium is established and all motion stops, which choice best describes the location of the block? The block is very small in comparison to the pool.

(A) The block is resting at the bottom of the pool.

(B) The block is completely submerged, but stops 75 % of the way to the bottom of the pool.

(C) The block is completely submerged, but stops 25 % of the way to the bottom of the pool.

(D) The block is floating with 75 % of its volume under the water's surface.

(E) The block is floating with 25 % of its volume under the water's surface.

A child's balloon is filled with pure Xenon gas. This balloon then is released fr om rest two meters above the ground on Earth. Which one of the following choices best describes the response of the balloon?

(A) The balloon immediately falls toward the ground.

(B) The balloon floats gently in the air, finally reaching the ground after several minutes.

(C) The balloon floats gently in the air, essentially hovering at the same height for at least a day.

(D) The balloon very, very slowly and gently rises upward.

(E) The balloon rapidly rises into the sky.

Water flows ideally through a cylindrically-shaped pipe. At the lower end, the pipe's cross-sectional area is 30.0 $cm^{2}$ whereas in the upper portion, the pipe's cross-sectional area is 10.0 $cm^{2}$ and fluid is moving at 9.0 $m/s$. Which one of the following choices best represents the difference in pressure between the lower section of the pipe and the upper section if the vertical distance between the centers of the pipe sections is 2.0 $m$?

(A) 5.6 $Pa$
(B) 6.05 $Pa$
(C) 56 $kPa$
(D) 60.5 $kPa$
(E) 65 $kPa$

An ideal fluid completely fills a small horizontal tube that has a narrowing cross-sectional area as seen in the figure. Which one of the following choices best describes what has happened to the fluid's speed and its associated pressure in the narrower region as compared to the wider region?

(A) The fluid speed increased and the fluid pressure decreased.

(B) The fluid speed increased and the fluid pressure increased.

(C) The fluid speed increased and the fluid pressure remained the same.

(D) The fluid speed decreased and the fluid pressure increases.

(E) The fluid speed decreased and the fluid pressure decreases.

A $\mathrm{U}$-tube is filled with mercury (density 13.6 $g/_{cm^{3}}$) as shown in the figure. Water of mass 800 grams is added to the left-hand side of the tube. When equilibrium is $\mathrm{r}\mathrm{e}$-established, the tube appears as shown in the right-most figure. The cross-sectional area of the left tube is 6.50 $cm^{2}$ while the right tube has cross-sectional area 15.0 $cm^{2}$. Which one of the following choices best represents the height x above the original equilibrium that the mercury rises in the right tube? The drawings are not to scale.

(A) 1.96 cm

(B) 2.74 cm

(C) 3.92 cm

(D) 4.92 cm

(E) 9.05 cm

A solid cube of iron and a solid cube of aluminum have equal mass. The cubes are placed into the same large pool of water so that each is completely submerged and resting on the pool's bottom. Which object experiences the greater buoyant force from the water?

(A) The iron cube

(B) The aluminum cube

(C) The buoyant forces are equal.

(D) The mass of the cubes is needed to answer the question.

(E) The answer depends on whether the pool is filled with fresh water or salt water.

A spring scale reads 2.50 $N$ when a small solid mass hangs from it in air. The spring scale reads 1.58 $N$ when the mass at the end of the spring is completely submerged in a container of water. Which one of the following choices best represents the density of the solid mass?

(A) $3.68\displaystyle \times 10^{3}\frac{kg}{m^{3}}$
(B) $2.72\displaystyle \times 10^{3}\frac{kg}{m^{3}}$
(C) $1.58\displaystyle \times 10^{3}\frac{kg}{m^{3}}$

(D) $9.20\displaystyle \times 10^{2}\frac{kg}{m^{3}}$
(E) $1.58\displaystyle \times 10^{2}\frac{kg}{m^{3}}$

At a party, two spherical balloons are expanded to have the same radius. Balloon # 1 is filled with helium gas while balloon # 2 is filled with xenon gas. Which one of the following statements about the buoyant forces on the balloons is correct?

(A) The buoyant force is greater for the helium balloon.

(B) The buoyant force is greater for the xenon balloon.

(C) The buoyant force is the same for each balloon.

(D) The balloon experiencing the greater buoyant force cannot be determined without knowing the radius.

(E) The balloon experiencing the greater buoyant force cannot be determined without knowing the atmospheric pressure at the time.

A large swimming pool is filled with a liquid having a density of $5.00\displaystyle \times 10^{2}\frac{kg}{m^{3}}$. A person wants to see what happens if she jumps into the deep end of the pool (3.0 meters deep). Which one of the following choices correctly identifies what will happen to the person? Assume that the person does not try to move their arms or legs until discovering what happens after equilibrium is established.

(A) The person will float with much more than 50% of their body's volume above the liquid's surface.

(B) The person will float with approximately 50% of their body's volume above the liquid's surface.

(C) The person will float with much less than 50% of their body's volume above the liquid's surface.

(D) The person will sink but remain off the bottom of the pool.

(E) The person will sink to the pool's bottom.

Water flows out of a horizontal drainpipe at the rate of 120 kg per minute. Its initial vertical velocity is zero and it falls 3.20 $\mathrm{m}$ to the ground. What is the average force it exerts when it hits the ground?

(A) 6.0 $\mathrm{N}$
(B) 10.0 $\mathrm{N}$
(C) 12.0 $\mathrm{N}$
(D) 16.0 $\mathrm{N}$
(E) 20.0 $\mathrm{N}$

A pine wood block is floating in a small pool. There is a second pine wood block that sits on top of the first and does not touch the water. If the top block is taken off and placed in the water, how does the new water level in the pool compare to the original water level?

(A) Rises

(B) Lowers

(C) Does not change

(D)It depends upon the size ofthe blocks

(E) It depends upon the amount of water in the pool.

A hole with a radius of 1.0 mm develops in the bottom of a 15 m tall tank filled to the top with water. The tank is open at the top. At what rate will water initially flow out of the hole?
(A) $5.4 \times 10^{-3} \mathrm{~m}^{3} / \mathrm{s}$
(B) $5.4 \times 10^{-4} \mathrm{~m}^{3} / \mathrm{s}$
(C) $5.4 \times 10^{-5} \mathrm{~m}^{3} / \mathrm{s}$
(D) $5.4 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{s}$
(E) $5.4 \times 10^{-7} \mathrm{~m}^{3} / \mathrm{s}$

A uniform wooden block is a rectangular prism with dimensions of $10 \mathrm{~cm} \times 6 \mathrm{~cm} \times 2 \mathrm{~cm}$. The block will be placed on a level table in one of three possible orientations with a side parallel to the tabletop. Let $P_{\mathrm{L}}$ equal the largest possible pressure the block can exert on the table and $P_{\mathrm{S}}$ equal the smallest possible pressure the block can exert on the table. What is the ratio $P_{\mathrm{L}} / P_{\mathrm{s}}$ ?
(A) $5 / 3$
(B) 3
(C) 5
(D) 9
(E) 25

What does a Venturi meter measure?
(A) fluid pressure
(B) fluid density
(C) fluid speed
(D) fluid flow
(E) fluid temperature

A block of wood is floating on water. If you push down on the block until it is completely submerged, the buoyant force acting on it
(A) increases.
(B) decreases.
(C) stays the same.
(D) is dependent upon the type of wood.
(E) is dependent upon the depth to which the block is pushed.

As an airplane is flying, it is determined that the airflow speed past the lower surface of the wing is $100 \mathrm{~m} / \mathrm{s}$. What speed of airflow over the upper surface of the wing would give a pressure difference of 1000 Pa ? $1.293 \frac{\mathrm{~kg}}{\mathrm{~m}^{3}}$ is the density of the air.
(A) $102 \mathrm{~m} / \mathrm{s}$
(B) $103 \mathrm{~m} / \mathrm{s}$
(C) $105 \mathrm{~m} / \mathrm{s}$
(D) $108 \mathrm{~m} / \mathrm{s}$
(E) $111 \mathrm{~m} / \mathrm{s}$

A beaker is filled with 800 mL of water. A wooden cylinder will be placed into the beaker. If the wood's density is $800 \frac{\mathrm{kg}}{\mathrm{m}^{3}}$, what mass cylinder will raise the water level to the beaker's maximum volume of 1000 mL?
(A) 100 g
(B) 160 g
(C) 200 g
(D) 250 g
(E) 360 g

A container filled with water is placed in an elevator. When the elevator is at rest, a small block floats in the water with 50% of its volume submerged. If the elevator accelerates up with a constant acceleration of 0.1 g , what percentage of the block's volume will be submerged? Treat water as an incompressible fluid.

(A) $5 \%$
(B) $45 \%$
(C) $50 \%$
(D) $55 \%$
(E) 95%