Question 1

Spherical particles of density 2.0 g/cm³ are shaken in a container of water (viscosity = 1.0 ´ 10^-3 N*s/m³).The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the radius of the largest particles still in suspension at that time?

Accepted Answer

The terminal velocity of a particle in a fluid is given by Stokes' Law: v = (2/9) * (r^2 * (ρ_p - ρ_f) * g) / η. Solving for r with given values and time, the largest radius is 4.5 x 10^-6 m.

Question 2

A fluid has a density of 1 040 kg/m³.If it rises to a height of 1.8 cm in a 1.0-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

Accepted Answer

Using the capillary rise equation: 
h = (2T cosθ)/(ρgr) 
where h = height of fluid rise, T = surface tension, θ = contact angle (zero in this case), ρ = density of fluid, g = acceleration due to gravity, r = radius of capillary tube 
Plugging in the given values: 
1.8 cm = (2T)/(1040 x 9.81 x 0.0005 cm) 
Solving for T: 
T = 0.046 N/m 
Therefore, the surface tension of the liquid is 0.046 N/m.

Question 3

A fluid is drawn up through a tube as shown below.The atmospheric pressure is the same at both ends.Use Bernoulli's equation to determine the speed of fluid flow out of the tank.If the height difference from the top of the tank to the bottom of the siphon is 1.0 m,then the speed of outflow is:

Accepted Answer

According to Bernoulli's equation, the pressure in the siphon must be lower than the pressure in the tank, and the speed of the fluid must increase as it flows from the tank to the siphon. Since the atmospheric pressure is the same at both ends, the difference in pressure is due to the difference in height between the top of the tank and the bottom of the siphon. The height difference is 1.0 m, so the speed of outflow can be calculated using the equation:

v^2 = 2gh

where v is the speed of outflow, g is the acceleration due to gravity (9.8 m/s^2), and h is the height difference. Plugging in the values, we get:

v^2 = 2(9.8)(1.0) = 19.6
v = √19.6 ≈ 4.4 m/s

Therefore, the best choice is C.

Question 4

A jet of water flowing from a hose at 15 m/s is directed against a wall.If the mass flow in the fluid stream is 2.0 kg/s,what force is the water applying to the wall if backsplash is negligible?

Accepted Answer

The force exerted by the water on the wall can be calculated using the formula F = Δp/Δt = m * v, where m is the mass flow rate and v is the velocity. Here, F = 2.0 kg/s * 15 m/s = 30 N.

Question 5

A pipe of diameter three cm is replaced by one of the same length but of diameter six cm.If the pressure difference between the ends of the pipe remains the same,by what factor is the rate of flow of a viscous liquid through it changed?

Accepted Answer

The rate of flow of a viscous liquid through a pipe is proportional to the fourth power of the diameter (Poiseuille's law). Doubling the diameter from 3 cm to 6 cm increases the flow rate by a factor of 2^4 = 16.

Question 6

It takes 2.0 minutes to fill a gas tank with 40 liters of gasoline.If the pump nozzle is 1.0 cm in radius,what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)

Accepted Answer

To find the average speed, use the formula: speed = volume flow rate / cross-sectional area. First, convert 40 liters to cubic meters: 40 liters = 0.040 m³. The time is 2 minutes = 120 seconds. The volume flow rate is 0.040 m³ / 120 s = 0.000333 m³/s. The cross-sectional area of the nozzle is πr² = π(0.01 m)² = 3.14 x 10^-4 m². The speed is 0.000333 m³/s / 3.14 x 10^-4 m² ≈ 1.1 m/s.

Question 7

A unit for viscosity,the centipoise,is equal to which of the following?

Accepted Answer

1 centipoise = 10^-3 N F1F1F1S1F1F1F10s/m²

Question 8

A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.0 cm diameter narrows to 1.0 cm diameter,what is the pressure drop in the constricted section for airflow of 3.0 m/s in the 2-cm section? (Assume air density is 1.25 kg/m³. )

Accepted Answer

The pressure drop can be calculated using Bernoulli's equation and the continuity equation. The velocity in the constricted section is 12 m/s. Using Bernoulli's equation, the pressure drop is calculated as 84 Pa.

Question 9

In order to overcome a surface tension of a fluid,a force of 1.32 ´ 10^-2 N is required to lift a wire ring of circumference 12.0 cm.What is the surface tension of the fluid?

Accepted Answer

Surface tension = Force required to lift the ring / Circumference of the ring= 1.32 ´ 10^-2 N / 12.0 cm= 0.055 N/m

Question 10

A pipe carrying water has a radius of 1.0 cm.If the flow velocity is 9.0 cm/s,which of the following characterizes the flow? Take the viscosity of water to be 1.0 ´ 10^-3 N*s/m.

Accepted Answer

The flow is characterized by the Reynolds number, which is calculated as Re = (density × velocity × diameter) / viscosity. For water, density is approximately 1000 kg/m³. Substituting the given values, Re is less than 2000, indicating streamlined flow.

Question 11

Spherical particles of density 2.0 g/cm³ are shaken in a container of water (viscosity = 1.0 ´ 10^-3 N*s/m³).The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the greatest terminal velocity of the particles still in suspension at that time?

Accepted Answer

The answer of Spherical particles of density 2.0 g/cm³ are...

Question 12

Water is sent from a fire hose at 30 m/s at an angle of 30 $\degree$above the horizontal.What is the maximum height reached by the water?

Accepted Answer

The answer of Water is sent from a fire hose...

Question 13

The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,which is 1.2 m in diameter.If the speed of flow is 3.0 m/s in the large-diameter pipe,determine the speed of flow in the test section.

Accepted Answer

The continuity equation states that mass flow rate must be conserved:

ρ₁A₁V₁ = ρ₂A₂V₂

where 
ρ₁ and ρ₂ are the densities at sections 1 and 2 respectively,
A₁ and A₂ are the areas at sections 1 and 2 respectively,
V₁ and V₂ are the velocities at sections 1 and 2 respectively.

Let's assume that the fluid is incompressible, so density is constant. We also know that the areas of the two sections are related by:

A₂ = (1/3)A₁

Hence, we can write:

V₂ = (A₁/A₂)V₁
V₂ = 3V₁

Substituting the given values:

V₂ = 3(3.0 m/s) = 9.0 m/s

Therefore, the correct answer is C) 27 m/s, since the velocity in the test section is three times that in the large-diameter pipe.

Question 14

A centrifuge rotates at 100 rev/s (i.e. ,628 rad/s).If the test tube places the suspension at 8.0 cm from the axis of rotation,by what factor are the terminal speeds of the settling particles increased as compared to sedimentation cause by gravity?

Accepted Answer

The centrifugal acceleration is given by $ a = \omega^2 \times r $. Substituting $ \omega = 628 \, \text{rad/s} $ and $ r = 0.08 \, \text{m} $, we find $ a \approx 3.2 \times 10^4 \, \text{m/s}^2 $. The factor increase compared to gravity ($ g = 9.8 \, \text{m/s}^2 $) is $ \frac{3.2 \times 10^4}{9.8} \approx 3.2 \times 10^3 $.

Question 15

Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?

Accepted Answer

When an object is falling through a fluid at its terminal speed, the upward drag force on the object becomes equal in magnitude to the downward gravitational force, resulting in a net force of zero. Therefore, the correct answer is D.

Question 16

How much air must be pushed downward at 40.0 m/s to keep an 800-kg helicopter aloft?

Accepted Answer

The answer of How much air must be pushed downward...

Question 17

The condition for onset of turbulent flow is that the Reynolds Number reaches what value?

Accepted Answer

The answer of The condition for onset of turbulent flow...

Question 18

Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.0 cm.If the nozzle has an opening of diameter 0.50 cm,and if the water leaves the nozzle at a speed of 10 m/s,what is the speed of the water inside the hose?

Accepted Answer

The speed of the water inside the hose can be found using the principle of conservation of mass (continuity equation). The flow rate must be constant, so A1V1 = A2V2. Solving for V1 gives V1 = (A2/A1) * V2 = (π(0.25)^2/π(1)^2) * 10 m/s = 0.63 m/s.

Question 19

A Boeing-737 airliner has a mass of 20 000 kg.The total area of the wings is 100 m².What must be the pressure difference between the top and bottom of the wings to keep the airplane up?

Accepted Answer

The pressure difference is given by the formula:$$\Delta p = \frac{2mg}{A}$$where:* $\Delta p$ is the pressure difference* $m$ is the mass of the airplane* $g$ is the acceleration due to gravity* $A$ is the total area of the wingsPlugging in the given values, we get:$$\Delta p = \frac{2(20 000 	ext{ kg})(9.8 	ext{ m/s}^2)}{100 	ext{ m}^2} = 3920 	ext{ Pa}$$Therefore, the pressure difference between the top and bottom of the wings must be 3920 Pa to keep the airplane up.

Question 20

How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls a vertical distance of 100 m?

Accepted Answer

The theoretical power available from a mass flow of water falling a vertical distance is given by the equation: 
Power = (mass flow rate) x g x h, 
where g is the acceleration due to gravity (9.81 m/s^2) and h is the height of the fall (in meters). 
Substituting the given values, 
Power = (1000 kg/s) x (9.81 m/s^2) x (100 m) 
Power = 981,000 W = 980 kW (rounded to the nearest whole number) 
Therefore, option A is the correct answer.

Quiz 9: Solids and Fluids

Spherical particles of density 2.0 g/cm³ are shaken in a container of water (viscosity = 1.0 ´ 10^-3 N*s/m³) .The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the radius of the largest particles still in suspension at that time?

A fluid has a density of 1 040 kg/m³.If it rises to a height of 1.8 cm in a 1.0-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

A fluid is drawn up through a tube as shown below.The atmospheric pressure is the same at both ends.Use Bernoulli's equation to determine the speed of fluid flow out of the tank.If the height difference from the top of the tank to the bottom of the siphon is 1.0 m,then the speed of outflow is:

A jet of water flowing from a hose at 15 m/s is directed against a wall.If the mass flow in the fluid stream is 2.0 kg/s,what force is the water applying to the wall if backsplash is negligible?

A pipe of diameter three cm is replaced by one of the same length but of diameter six cm.If the pressure difference between the ends of the pipe remains the same,by what factor is the rate of flow of a viscous liquid through it changed?

It takes 2.0 minutes to fill a gas tank with 40 liters of gasoline.If the pump nozzle is 1.0 cm in radius,what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)

A unit for viscosity,the centipoise,is equal to which of the following?

A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.0 cm diameter narrows to 1.0 cm diameter,what is the pressure drop in the constricted section for airflow of 3.0 m/s in the 2-cm section? (Assume air density is 1.25 kg/m³. )

In order to overcome a surface tension of a fluid,a force of 1.32 ´ 10^-2 N is required to lift a wire ring of circumference 12.0 cm.What is the surface tension of the fluid?

A pipe carrying water has a radius of 1.0 cm.If the flow velocity is 9.0 cm/s,which of the following characterizes the flow? Take the viscosity of water to be 1.0 ´ 10^-3 N*s/m.

Spherical particles of density 2.0 g/cm³ are shaken in a container of water (viscosity = 1.0 ´ 10^-3 N*s/m³) .The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the greatest terminal velocity of the particles still in suspension at that time?

Water is sent from a fire hose at 30 m/s at an angle of 30 $\degree$ above the horizontal.What is the maximum height reached by the water?

The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,which is 1.2 m in diameter.If the speed of flow is 3.0 m/s in the large-diameter pipe,determine the speed of flow in the test section.

A centrifuge rotates at 100 rev/s (i.e. ,628 rad/s) .If the test tube places the suspension at 8.0 cm from the axis of rotation,by what factor are the terminal speeds of the settling particles increased as compared to sedimentation cause by gravity?

Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?

How much air must be pushed downward at 40.0 m/s to keep an 800-kg helicopter aloft?

The condition for onset of turbulent flow is that the Reynolds Number reaches what value?

Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.0 cm.If the nozzle has an opening of diameter 0.50 cm,and if the water leaves the nozzle at a speed of 10 m/s,what is the speed of the water inside the hose?

A Boeing-737 airliner has a mass of 20 000 kg.The total area of the wings is 100 m².What must be the pressure difference between the top and bottom of the wings to keep the airplane up?

How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls a vertical distance of 100 m?

Quiz 9: Solids and Fluids

Spherical particles of density 2.0 g/cm3 are shaken in a container of water (viscosity = 1.0 ´ 10-3 N*s/m3) .The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the radius of the largest particles still in suspension at that time?

A fluid has a density of 1 040 kg/m3.If it rises to a height of 1.8 cm in a 1.0-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

A fluid is drawn up through a tube as shown below.The atmospheric pressure is the same at both ends.Use Bernoulli's equation to determine the speed of fluid flow out of the tank.If the height difference from the top of the tank to the bottom of the siphon is 1.0 m,then the speed of outflow is:

A jet of water flowing from a hose at 15 m/s is directed against a wall.If the mass flow in the fluid stream is 2.0 kg/s,what force is the water applying to the wall if backsplash is negligible?

A pipe of diameter three cm is replaced by one of the same length but of diameter six cm.If the pressure difference between the ends of the pipe remains the same,by what factor is the rate of flow of a viscous liquid through it changed?

It takes 2.0 minutes to fill a gas tank with 40 liters of gasoline.If the pump nozzle is 1.0 cm in radius,what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)

A unit for viscosity,the centipoise,is equal to which of the following?

A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.0 cm diameter narrows to 1.0 cm diameter,what is the pressure drop in the constricted section for airflow of 3.0 m/s in the 2-cm section? (Assume air density is 1.25 kg/m3. )

In order to overcome a surface tension of a fluid,a force of 1.32 ´ 10-2 N is required to lift a wire ring of circumference 12.0 cm.What is the surface tension of the fluid?

A pipe carrying water has a radius of 1.0 cm.If the flow velocity is 9.0 cm/s,which of the following characterizes the flow? Take the viscosity of water to be 1.0 ´ 10-3 N*s/m.

Spherical particles of density 2.0 g/cm3 are shaken in a container of water (viscosity = 1.0 ´ 10-3 N*s/m3) .The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the greatest terminal velocity of the particles still in suspension at that time?

Water is sent from a fire hose at 30 m/s at an angle of 30 °\degree° above the horizontal.What is the maximum height reached by the water?

The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,which is 1.2 m in diameter.If the speed of flow is 3.0 m/s in the large-diameter pipe,determine the speed of flow in the test section.

A centrifuge rotates at 100 rev/s (i.e. ,628 rad/s) .If the test tube places the suspension at 8.0 cm from the axis of rotation,by what factor are the terminal speeds of the settling particles increased as compared to sedimentation cause by gravity?

Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?

How much air must be pushed downward at 40.0 m/s to keep an 800-kg helicopter aloft?

The condition for onset of turbulent flow is that the Reynolds Number reaches what value?

Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.0 cm.If the nozzle has an opening of diameter 0.50 cm,and if the water leaves the nozzle at a speed of 10 m/s,what is the speed of the water inside the hose?

A Boeing-737 airliner has a mass of 20 000 kg.The total area of the wings is 100 m2.What must be the pressure difference between the top and bottom of the wings to keep the airplane up?

How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls a vertical distance of 100 m?

Spherical particles of density 2.0 g/cm³ are shaken in a container of water (viscosity = 1.0 ´ 10^-3 N*s/m³) .The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the radius of the largest particles still in suspension at that time?

A fluid has a density of 1 040 kg/m³.If it rises to a height of 1.8 cm in a 1.0-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.0 cm diameter narrows to 1.0 cm diameter,what is the pressure drop in the constricted section for airflow of 3.0 m/s in the 2-cm section? (Assume air density is 1.25 kg/m³. )

In order to overcome a surface tension of a fluid,a force of 1.32 ´ 10^-2 N is required to lift a wire ring of circumference 12.0 cm.What is the surface tension of the fluid?

A pipe carrying water has a radius of 1.0 cm.If the flow velocity is 9.0 cm/s,which of the following characterizes the flow? Take the viscosity of water to be 1.0 ´ 10^-3 N*s/m.

Spherical particles of density 2.0 g/cm³ are shaken in a container of water (viscosity = 1.0 ´ 10^-3 N*s/m³) .The water is 8.0 cm deep and is allowed to stand for 30 minutes.What is the greatest terminal velocity of the particles still in suspension at that time?

Water is sent from a fire hose at 30 m/s at an angle of 30 $\degree$ above the horizontal.What is the maximum height reached by the water?

A Boeing-737 airliner has a mass of 20 000 kg.The total area of the wings is 100 m².What must be the pressure difference between the top and bottom of the wings to keep the airplane up?