Fluid Statics Archives • Nerd Notes

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What we found:

A block of iron, which has a density that is greater than the density of water, is at rest on the bottom of a pool. Which of the following claims about the magnitude of the normal force on the block and the weight of the block is true?

A raft of density \( 0.7 \rho_{w} \) floats partially submerged in a body of water of density \( \rho_{w} \). The raft has dimensions of length \( L \), width \( W \), and height \( H \), as shown in the figure. The height of the raft beneath the surface of the water is \( h \). Which of the following expressions is equal to \( h \)?

A large, empty plastic jug with mass \( m_j \) and volume \( V_j \) floats in a pool of water, as shown in the figure. If the density of water is \( \rho_w \), which of the following expressions is equal to the volume of water \( V_w \) that must be added to the jug so that the top of the jug will be at the level of the water?

Why is fluid pressure considered a scalar quantity, even though it is defined using force \( P = \frac{F_{\perp}}{A} \), which is a vector?

The absolute pressure at a certain point in a lake is \( P_{abs} \). If the local atmospheric pressure is \( P_{atm} \), which expression represents the gauge pressure \( P_{gauge} \) at that point?

A cube is fully submerged at a depth of \( 1 \) \( \text{m} \) in a large tank of water. It is then moved to a depth of \( 3 \) \( \text{m} \). How does the buoyant force on the cube at \( 3 \) \( \text{m} \) compare to the buoyant force at \( 1 \) \( \text{m} \)?

A student measures the weight of an irregularly shaped metal object in air and finds it to be \( 15 \) \( \text{N} \). When the object is fully submerged in water, its apparent weight is \( 10 \) \( \text{N} \). What is the magnitude of the buoyant force acting on the object?

The gauge pressure at a certain depth in a fluid is \( P_{gauge} \). If you dive to a depth that is twice as deep in the same fluid, what will the new gauge pressure be?

Which of the following is a scalar quantity?

If a perpendicular force \( F \) is applied to a surface area \( A \), resulting in a pressure \( P \), what is the new pressure if the force is doubled and the area is quadrupled?

According to the microscopic description of fluids, what is the fundamental cause of the pressure exerted by a fluid on the walls of its container?

A cube of side length \( L \) is completely submerged in a fluid of density \( \rho \). The top of the cube is at a depth \( d \). What is the magnitude of the net force exerted by the fluid on the two vertical side faces of the cube?

Which of the following best describes the implication of an ideal fluid being ‘incompressible’?

Why does the pressure of the Earth’s atmosphere decrease as you move to a higher altitude, and how does this relate to the definition of an ideal fluid?

Which of the following best describes ‘gauge pressure’ at a certain depth in a static fluid?

If the absolute pressure at a depth of \( 10 \) \( \text{m} \) in a lake is \( 2 \) \( \text{atm} \), what would the absolute pressure be at a depth of \( 20 \) \( \text{m} \) in the same lake? (Assume \( 1 \) \( \text{atm} \) is the surface pressure).

A student monitors the gauge pressure at the bottom of a cylinder filled with water. If the student pours out half of the water and replaces it with an equal volume of oil (which is less dense than water and does not mix), how does the gauge pressure at the bottom change?

A student measures the pressure at the bottom of a vertical column of liquid to be \( P_{total} \). If the atmospheric pressure \( P_{atm} \) doubles, what happens to the gauge pressure at the bottom of that same column?

Which of the following statements correctly characterizes the nature of pressure \( P \) as a physical quantity within a fluid?

A student is asked to calculate the pressure at the bottom of three different shaped vessels: a cylinder, a cone (wide base), and a funnel (narrow base). All three are filled with the same liquid to the exact same height \( H \). Which vessel has the highest pressure at the bottom?

A student creates a graph of Absolute Pressure \( P \) on the vertical axis versus Depth \( h \) on the horizontal axis for a static, incompressible liquid. What does the slope of this graph represent?

Two identical containers are filled to the same height. Container A is filled with water \( \rho_w \), and Container B is filled with oil \( \rho_o \), where \( \rho_w > \rho_o \). How does the gauge pressure at the bottom of Container A compare to the gauge pressure at the bottom of Container B?

A U-tube contains a liquid of density \( \rho \). One arm of the U-tube is sealed, trapping a volume of air, while the other arm remains open to the atmosphere. Initially, the liquid levels are equal. If more of the same liquid is added to the open arm, how will the new equilibrium levels compare?

Consider a U-shaped tube open to the atmosphere on both ends, filled with an ideal fluid. If a piston of mass \( M \) and area \( A \) is placed on the right arm, what is the difference in height \( \Delta h \) between the fluid levels in the two arms?

An object is weighted in air and found to have a weight \( W_{\text{air}} \). When fully submerged in an open container of water, its apparent weight is \( W_{\text{app}} \). If the container is now moved to a location with higher atmospheric pressure, how will the apparent weight \( W_{\text{app}} \) change?

A U-tube is filled with water and is being accelerated horizontally to the right with a constant acceleration \( a \). Which of the following describes the behavior of the water levels in the two vertical arms of the U-tube?

An airtight container is completely filled with an ideal, incompressible fluid. If the external pressure on the container is increased by \( \Delta P \), how does the pressure change at a point located at the very bottom of the container?

A U-tube with a uniform cross-section is open to the atmosphere and filled with water. A piston is placed in the left arm and pushed down with a constant force \( F \). If the right arm remains open, what is the difference in height \( \Delta h \) between the water levels in the two arms?

A U-tube open to the atmosphere at both ends is partially filled with water of density \( \rho_w \). Oil of density \( \rho_o \) (where \( \rho_o < \rho_w \)) is poured into the left arm until it forms a column of height \( L \). The interface between the oil and water in the left arm is found to be a vertical distance \( d \) below the water surface in the right arm. Which of the following expressions correctly represents the density of the oil?

A student uses a mercury barometer to measure atmospheric pressure. If the student replaces the original tube with one that has \( 2 \) times the cross-sectional area, how will the height \( h \) of the mercury column change?

Three containers have the same base area \( A \) and are filled with water to the same height \( h \), but they have different shapes: one is cylindrical, one widens toward the top, and one narrows toward the top. Which of the following is true regarding the gauge pressure \( P \) at the bottom and the total force \( F \) exerted by the fluid on the base?

A tube contains a volume of water and a volume of mercury as shown in the figure above. Both ends of the tube are open. Points A and B are at the same level and points C and D are at the same level. The distances between points A and B and the surface of the liquids are indicated: the vertical distance from the water surface to point A is \( 0.15 \) \( \text{m} \), and the vertical distance from the mercury surface to point B is \( 0.01 \) \( \text{m} \). Which of the following correctly relates the gauge pressures at the points shown? The density of the water is \( 1{,}000 \) \( \text{kg/m}^3 \) and the density of the mercury is \( 13{,}600 \) \( \text{kg/m}^3 \).

A person uses a straw to drink water from a cup. Which of the following best describes the physics of how the water moves up the straw?

A sphere of mass \( M \) and volume \( V \) is suspended from a spring scale and completely submerged in a fluid of density \( \rho_f \). What is the reading on the spring scale?

A student wants to determine the density of an unknown liquid. They have a block of known density \( \rho_b \) and volume \( V \). When the block is placed in the liquid, it sinks and rests on the bottom. A spring scale attached to the block reads a tension \( T \). Which formula should the student use to find the liquid density \( \rho_L \)?

A tube contains a volume of water and a volume of mercury as shown in the figure above. Both ends of the tube are open. Points \( A \) and \( B \) are at the same level and points \( C \) and \( D \) are at the same level. The distance between points \( A \) and \( B \) and the surface of the liquids are shown. Which of the following correctly relates the gauge pressures at the points shown? The density of the water is \( 1{,}000 \) \( \text{kg/m}^3 \) and the density of the mercury is \( 13{,}600 \) \( \text{kg/m}^3 \).

A student places a wooden block of mass \( m \) in a container of water. The block floats with half of its volume above the surface of the water. The student then begins to stack small objects on top of the block until the wooden block is completely submerged but none of the objects stacked on top are submerged. What is the buoyant force acting on the block now?

A cube of side length \( s \) rests on the bottom surface of a container of fluid as shown in the figure. The fluid is at a height \( y \) above the bottom of the tank. The fluid has density \( \rho \) and the atmospheric pressure is \( P_{\text{atm}} \).Which of the following expressions is equal to the absolute pressure exerted by the fluid on the top surface of the cube?

The diagram below shows a hydraulic chamber with a spring \( (k_s = 1250 \, \text{N/m}) \) attached to the input piston and a rock of mass \( 55.2 \, \text{kg} \) resting on the output plunger. The input piston and output plunger are at about the same height, and each has negligible mass. The chamber is filled with water.

Marc’s favorite ride at Busch Gardens is the Flying Umbrella, which is lifted by a hydraulic jack. The operator activates the ride by applying a force of \( 72 \) \( \text{N} \) to a \( 30 \)\( \text{cm}^2 \) cylindrical piston, which holds the \( 20,000 \)\( \text{N} \) ride off the ground. What is the area of the piston that holds the ride?

Johnny the auto mechanic is raising a \( 1200 \) \( \text{kg} \) car on her hydraulic lift so that she can work underneath. If the area of the input piston is \( 12 \) \( \text{cm}^2 \), while the output piston has an area of \( 700 \) \( \text{cm}^2 \), what force must be exerted on the input piston to lift the car?

When the button of a trash compactor is pushed, a force of \( 350 \) \( \text{N} \) pushes down on a \( 1.3 \) \( \text{cm}^2 \) input piston, creating a force of \( 22,076 \) \( \text{N} \) to crush the trash. What is the area of the piston that crushes the trash?

A trash compactor pushes down with a force of \( 500 \) \( \text{N} \) on a \( 3 \) \( \text{cm}^2 \) input piston, causing a force of \( 30,000 \) \( \text{N} \) to crush the trash. What is the area of the output piston that crushes the trash?

The large piston in a hydraulic lift has a radius of \( 250 \) \( \text{cm}^2 \). What force must be applied to the small piston with a radius of \( 25 \) \( \text{cm}^2 \) in order to raise a car of mass \( 1500 \) \( \text{kg} \)?

The difference in pressure between the atmosphere and the human lungs is \( 1.05 \times 10^5 \) \( \text{Pa} \). What is the longest straw you could use to draw up milk whose density is \( 1030 \) \( \text{kg/m}^3 \)?

Ben’s favorite ride at the Barrel-O-Fun Amusement Park is the Flying Umbrella, which is lifted by a hydraulic jack. The operator activates the ride by applying a force of \( 72 \) \( \text{N} \) to a \( 3.0 \) \( \text{cm} \) wide cylindrical piston, which holds the \( 20,000 \) \( \text{N} \) ride off the ground. What is the diameter of the piston that holds the ride?

Rex, an auto mechanic, is raising a \( 1200 \) \( \text{kg} \) car on his hydraulic lift so that he can work underneath. If the area of the input piston is \( 12.0 \) \( \text{cm}^2 \), while the output piston has an area of \( 700 \) \( \text{cm}^2 \), what force must be exerted on the input piston to lift the car?

Nancy is using a turkey baster (a kitchen tool with a rubber bulb on one end and a tube on the other) to collect juices from a roasting turkey. When she squeezes and then releases the rubber bulb, it creates suction with a pressure of \( 99{,}800 \) \( \text{Pa} \). This suction causes the turkey juice to rise \( 9 \) \( \text{cm} \) up the tube. Based on this information, what is the density of the turkey juice?

Diamond has a density of \( 3500 \) \( \text{kg/m}^3 \). During a physics lab, a diamond drops out of Virginia’s necklace and falls into her graduated cylinder filled with \( 5.00 \times 10^{-5} \) \( \text{m}^3 \) of water. This causes the water level to rise to the \( 5.05 \times 10^{-5} \) \( \text{m}^3 \) mark. What is the mass of Virginia’s diamond?

Wanda watches the fish in her fish tank and notices that the angelfish like to feed at the water’s surface, while the catfish feed \( 0.300 \) \( \text{m} \) below at the bottom of the tank. If the average density of the water in the tank is \( 1000. \) \( \text{kg/m}^3 \), what is the pressure on the catfish?