Question 1

Water (density = 1.00 × 10³ kg/m³)flows at 7.2 m/s through a pipe with radius 0.025 m.The pipe goes up to the second floor of the building,2.00 m higher,and the pressure remains unchanged.What is the radius of the pipe on the second floor? A)0.019 m B)0.036 m C)0.0013 m D)0.23 m E)0.022 m

Accepted Answer

Using Bernoulli's Equation:
1/2ρv1² + ρgh1 + P1 = 1/2ρv2² + ρgh2 + P2
Assuming h1 = 0, P1 = P2, and solving for v2:
v2 = sqrt(2gh2 + (v1²/2))
At the second floor, the volume flow rate must remain constant:
A1v1 = A2v2
pi(0.025²)(7.2) = pi(r²)(sqrt(2g(2)))
r = 0.036 m

Question 2

A block of wood has specific gravity 0.80.When placed in water,what percent of the volume of the wood is above the surface?
A)0,the block sinks.
B)20%
C)80%
D)50%
E)100%

Accepted Answer

Specific gravity is the ratio of the density of the object to the density of water. Here, specific gravity of the block of wood is given as 0.80. This means that the density of the block of wood is 0.80 times the density of water.
When an object is placed in water, it displaces a volume of water equal to its own volume. If the displaced volume of water is more than the volume of the object, the object floats, and if it is less than the volume of the object, the object sinks.
Since the block of wood has a lower density than water, it displaces a volume of water that is greater than its own volume. Therefore, the block of wood floats. The percent of the volume of the wood above the surface is equal to the fraction of the volume of the block that is above the waterline. This fraction is equal to the ratio of the density of air to the density of water, which is approximately 0.20 or 20%.

Question 3

Water pressurized to 3.00 × 10⁵ Pa is flowing at 5.25 m/s in a pipe which contracts to 1/2 of its former area.What are the pressure and speed of the water after the contraction? (Density of water = 1 × 10³ kg/m³. ) A)2.59E+5 Pa,10.5 m/s B)3.00E+5 Pa,2.63 m/s C)3.00E+5 Pa,10.5 m/s D)4.59E+5 Pa,10.5 m/s E)2.59E+5 Pa,2.63 m/s

Accepted Answer

Using the principle of conservation of mass and Bernoulli's equation, the speed doubles to 10.5 m/s after the contraction, and the pressure decreases to 2.59E+5 Pa.

Question 4

It takes 4.00 minutes to fill a gas tank with 50.0 liters of gasoline.If the pump nozzle is 1.35 cm in radius,what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)
A)3.64 m/s
B)0.364 m/s
C)21.8 m/s
D)1.36 m/s
E)12.5 m/s

Accepted Answer

The answer of It takes 4.00 minutes to fill a...

Question 5

A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.00 cm diameter narrows to 1.00 cm diameter,what is the pressure drop in the constricted section for airflow of 2.16 m/s in the 2.00-cm section? (Assume air density is 1.25 kg/m³. ) A)11.7 Pa B)43.7 Pa C)45.7 Pa D)20.3 Pa E)87.5 Pa

Accepted Answer

The pressure drop in the constricted section can be calculated using the Bernoulli's equation and the continuity equation. The continuity equation gives us the relationship between the velocities and cross-sectional areas at two points in a flow, $A_1V_1 = A_2V_2$, where $A$ is the area and $V$ is the velocity. Given the diameters, we can find the areas of the sections, $A_1 = \pi(0.02/2)^2$ m$^2$ and $A_2 = \pi(0.01/2)^2$ m$^2$. Using the given velocity in the 2.00-cm section, we can find the velocity in the 1.00-cm section using the continuity equation. Then, applying Bernoulli's equation, we find the pressure difference ($\Delta P$) between the two sections. The calculation involves using the air density ($1.25 kg/m^3$), and the velocities in both sections to find $\Delta P$, which results in a pressure drop of 43.7 Pa.

Question 6

An ideal fluid,of density 850 kg/m³,flows at 0.560 kg/s through a pipe of radius 0.0250 m.What is the fluid speed? A)0.773 m/s B)0.00419 m/s C)285 m/s D)0.336 m/s E)0.599 m/s

Accepted Answer

The answer of An ideal fluid,of density 850 kg/m³,flows at...

Question 7

A heavily loaded boat is floating in a pond.The boat sinks because of a leak.What happens to the surface level of the pond?
A)It stays the same.
B)It goes up.
C)It goes down.
D)More information is needed to reach a conclusion.

Accepted Answer

The weight of the boat and its contents is displacing water and the volume of water being displaced is equal to the weight of the boat. When the boat sinks, that displaced water is no longer being held up by the boat, causing the overall volume of displaced water to decrease. This decrease in volume will cause the surface level of the pond to go down.

Question 8

The equation of continuity applied to an incompressible ideal fluid flowing through a pipe of varying diameter is based on what of the following being conserved for the fluid in the pipe?
A)its kinetic energy
B)its momentum
C)its flow rate
D)its potential energy

Accepted Answer

The equation of continuity states that mass flow rate is conserved for an incompressible fluid flowing through a pipe of varying diameter. This means that the product of the fluid's density, velocity, and cross-sectional area is constant along the pipe, so the flow rate must also be constant. Therefore, choice C is the correct option. Kinetic energy, momentum, and potential energy may change along the pipe due to changes in velocity and elevation, but they are not conserved quantities for the fluid in this situation.

Question 9

A heavily loaded boat is floating in a pond.The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under although it is now deeper in the water.What happens to the surface level of the pond?
A)It stays the same.
B)It goes up.
C)It goes down.
D)More information is needed to reach a conclusion.

Accepted Answer

The surface level of the pond will stay the same because the weight of the boat and the water displaced by the boat are still the same, even though the boat is deeper in the water now.

Question 10

A syringe has an inside radius of its barrel of 0.50 cm and at the opening at the end of the needle the radius is 1.0 mm.If a force F is applied to the plunger,what is the force produced at the opening of the needle?
A)5F
B)25F
C)F/5
D)F/25

Accepted Answer

The answer of A syringe has an inside radius of...

Question 11

Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.25 cm.If the nozzle has an opening of diameter 1.30 cm,and if the water leaves the nozzle at a speed of 14.0 m/s,what is the speed of the water inside the hose?
A)4.67 m/s
B)41.9 m/s
C)2.38 m/s
D)5.67 m/s
E)also 14.0 m/s

Accepted Answer

The speed of the water inside the hose can be found using the principle of conservation of mass, which implies that the flow rate (volume per time) must be constant throughout the hose. This can be expressed as $A_1v_1 = A_2v_2$, where $A_1$ and $A_2$ are the cross-sectional areas of the hose and nozzle, respectively, and $v_1$ and $v_2$ are the velocities of the water in the hose and nozzle, respectively. Given that $v_2 = 14.0 \, \text{m/s}$ and the diameters of the hose and nozzle, we can find $v_1$ by calculating the areas and rearranging the equation to solve for $v_1$. The area of a circle is given by $\pi r^2$, so the areas of the hose and nozzle can be calculated using their respective diameters ($d = 2r$). Substituting the given values and solving for $v_1$ yields a speed of 4.67 m/s inside the hose.

Question 12

The flow rate of a liquid through a 4.0-cm-radius pipe is 0.0080 m³/s.The average fluid speed in the pipe is A)0.040 m/s. B)0.0050 m/s. C)0.16 m/s. D)1.6 m/s. E)16 m/s.

Accepted Answer

The answer of The flow rate of a liquid through...

Question 13

A blimp is filled with 440 m³ of helium.How big a payload can the balloon lift? (The density of air is 1.29 kg/m³;the density of helium is 0.178 kg/m³. ) A)396 kg B)568 kg C)78.3 kg D)489 kg E)646 kg

Accepted Answer

The answer of A blimp is filled with 440 m³...

Question 14

Water (density = 1.00 × 10³ kg/m³)flows at 15.0 m/s through a pipe with radius 0.0400 m.The pipe goes up to the second floor of the building,2.50 m higher,and the pressure remains unchanged.What is the speed of the water flow in the pipe on the second floor? A)13.3 m/s B)16.6 m/s C)176 m/s D)14.2 m/s E)6.63 m/s

Accepted Answer

To solve this problem, we use the Bernoulli's equation, which in one of its forms can be written as $P_1 + \frac{1}{2}\rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho gh_2$. Given that the pressure remains unchanged and the change in height is 2.5 m, we can simplify the equation to $\frac{1}{2}\rho v_1^2 + \rho gh_1 = \frac{1}{2}\rho v_2^2 + \rho gh_2$. Solving for $v_2$ with the given values ($v_1 = 15.0 m/s$, $h_2 - h_1 = 2.5 m$, $\rho = 1000 kg/m^3$, $g = 9.8 m/s^2$) gives a result of approximately 13.3 m/s.

Question 15

A hole is poked through the metal side of a drum holding water.The hole is 16.0 cm below the water surface.What is the initial speed of outflow?
A)1.77 m/s
B)17.7 m/s
C)0.566 m/s
D)3.14 m/s
E)1.25 m/s

Accepted Answer

The initial speed of outflow can be calculated using Torricelli's law, which states that the speed $v$ of fluid flowing out of a hole at depth $h$ below the surface of the liquid is given by $v = \sqrt{2gh}$, where $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Plugging in the given depth $h = 16.0 \, \text{cm} = 0.16 \, \text{m}$, we get $v = \sqrt{2 \times 9.8 \, \text{m/s}^2 \times 0.16 \, \text{m}} \approx 1.77 \, \text{m/s}$.

Question 16

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 4.0 inches,respectively.The speed of the fluid flow through the 4.0-inch section will be what factor times that through the 1.0-inch section?
A)16
B)8
C)15
D) 
E)​

Accepted Answer

The answer of An ideal fluid flows through a pipe...

Question 17

An ideal fluid,of density 900 kg/m³,flows at 4.80 m/s through a level pipe with radius of 0.22 cm.The pressure in the fluid is 1.3 × 10⁵ N/m².This pipe connects to a second level pipe,with radius of 0.72 cm.Find the speed of flow in the second pipe. A)51 m/s B)1.5 m/s C)0.45 m/s D)16 m/s E)4.9 m/s

Accepted Answer

We can use the principle of continuity, which states that the mass flow rate (ρAv) of an ideal fluid is constant along a horizontal pipe. So, we can write:

ρ1A1v1 = ρ2A2v2

where ρ1 and ρ2 are the densities of the fluid in the first and second pipes, respectively; A1 and A2 are the cross-sectional areas of the pipes; v1 and v2 are the speeds of flow in the first and second pipes, respectively.

Since the fluid is ideal, its density is constant. Therefore, we can simplify the above equation to:

A1v1 = A2v2

Solving for v2, we get:

v2 = (A1/A2) v1

Substituting the given values, we get:

v2 = (π(0.22 cm)² / π(0.72 cm)²)(4.80 m/s) = 0.45 m/s

Therefore, the answer is (C) 0.45 m/s.

Question 18

Think of Bernoulli's equation as it pertains to an ideal fluid flowing through a horizontal pipe.Imagine that you take measurements along the pipe in the direction of fluid flow.What happens to the sum of the pressure and energy per unit volume?
A)It increases as the pipe diameter increases.
B)It decreases as the pipe diameter increases.
C)It remains constant as the pipe diameter increases.
D)No choices above are valid.

Accepted Answer

According to Bernoulli's equation, the sum of the pressure and energy per unit volume remains constant along a horizontal pipe when there is no change in height or acceleration due to gravity. Therefore, it does not depend on the diameter of the pipe.

Question 19

A large stone is resting on the bottom of the swimming pool.The normal force of the bottom of the pool on the stone is equal to the
A)weight of the stone.
B)weight of the water displaced.
C)sum of the weight of the stone and the weight of the displaced water.
D)difference between the weight of the stone and the weight of the displaced water.

Accepted Answer

The normal force is the difference between the weight of the stone and the buoyant force, which is equal to the weight of the displaced water.

Question 20

Water comes down the spillway of a dam from an initial vertical height of 170 m.What is the highest possible speed of the water at the end of the spillway?
A)5.89 m/s
B)18.4 m/s
C)57.7 m/s
D)1 670 m/s
E)3 330 m/s

Accepted Answer

The height h of the water can be used to calculate the potential energy, which is converted to kinetic energy at the bottom of the spillway. The kinetic energy equation is:

KE = 1/2 * m * v^2

where m is the mass of the water (which we can assume to be 1 kg per unit volume) and v is the velocity.

Using conservation of energy, we can set the potential energy at the top of the spillway (mgh) equal to the kinetic energy at the bottom (1/2 * mv^2):

mgh = 1/2 * mv^2

Canceling out the mass, we get:

gh = 1/2 * v^2

Solving for v, we get:

v = sqrt(2gh)

Plugging in the values given, we get:

v = sqrt(2*9.8*170) = 57.7 m/s

Therefore, the highest possible speed of the water at the end of the spillway is 57.7 m/s, which is choice C.

Quiz 9: Fluids and Solids

Water (density = 1.00 × 10³ kg/m³) flows at 7.2 m/s through a pipe with radius 0.025 m.The pipe goes up to the second floor of the building,2.00 m higher,and the pressure remains unchanged.What is the radius of the pipe on the second floor?

A block of wood has specific gravity 0.80.When placed in water,what percent of the volume of the wood is above the surface?

Water pressurized to 3.00 × 10⁵ Pa is flowing at 5.25 m/s in a pipe which contracts to 1/2 of its former area.What are the pressure and speed of the water after the contraction? (Density of water = 1 × 10³ kg/m³. )

It takes 4.00 minutes to fill a gas tank with 50.0 liters of gasoline.If the pump nozzle is 1.35 cm in radius,what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)

A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.00 cm diameter narrows to 1.00 cm diameter,what is the pressure drop in the constricted section for airflow of 2.16 m/s in the 2.00-cm section? (Assume air density is 1.25 kg/m³. )

An ideal fluid,of density 850 kg/m³,flows at 0.560 kg/s through a pipe of radius 0.0250 m.What is the fluid speed?

A heavily loaded boat is floating in a pond.The boat sinks because of a leak.What happens to the surface level of the pond?

The equation of continuity applied to an incompressible ideal fluid flowing through a pipe of varying diameter is based on what of the following being conserved for the fluid in the pipe?

A heavily loaded boat is floating in a pond.The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under although it is now deeper in the water.What happens to the surface level of the pond?

A syringe has an inside radius of its barrel of 0.50 cm and at the opening at the end of the needle the radius is 1.0 mm.If a force F is applied to the plunger,what is the force produced at the opening of the needle?

Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.25 cm.If the nozzle has an opening of diameter 1.30 cm,and if the water leaves the nozzle at a speed of 14.0 m/s,what is the speed of the water inside the hose?

The flow rate of a liquid through a 4.0-cm-radius pipe is 0.0080 m³/s.The average fluid speed in the pipe is

A blimp is filled with 440 m³ of helium.How big a payload can the balloon lift? (The density of air is 1.29 kg/m³;the density of helium is 0.178 kg/m³. )

Water (density = 1.00 × 10³ kg/m³) flows at 15.0 m/s through a pipe with radius 0.0400 m.The pipe goes up to the second floor of the building,2.50 m higher,and the pressure remains unchanged.What is the speed of the water flow in the pipe on the second floor?

A hole is poked through the metal side of a drum holding water.The hole is 16.0 cm below the water surface.What is the initial speed of outflow?

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 4.0 inches,respectively.The speed of the fluid flow through the 4.0-inch section will be what factor times that through the 1.0-inch section?

An ideal fluid,of density 900 kg/m³,flows at 4.80 m/s through a level pipe with radius of 0.22 cm.The pressure in the fluid is 1.3 × 10⁵ N/m².This pipe connects to a second level pipe,with radius of 0.72 cm.Find the speed of flow in the second pipe.

Think of Bernoulli's equation as it pertains to an ideal fluid flowing through a horizontal pipe.Imagine that you take measurements along the pipe in the direction of fluid flow.What happens to the sum of the pressure and energy per unit volume?

A large stone is resting on the bottom of the swimming pool.The normal force of the bottom of the pool on the stone is equal to the

Water comes down the spillway of a dam from an initial vertical height of 170 m.What is the highest possible speed of the water at the end of the spillway?