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 15 minutes. What is the greatest terminal velocity of the particles still in suspension at that time? A) 0.55 *10^-⁵ m/s B) 1.1 *10^-⁵ m/s C) 4.4 *10^-⁵ m/s D) 8.8 *10^-⁵ m/s

Accepted Answer

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

Question 2

Spherical particles of density 3.0 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) 4.5 *10^-⁶ m B) 9.0 *10^-⁶ m C) 2.6 *10^-⁶ m D) 5.6 *10^-⁶ m

Accepted Answer

The answer of Spherical particles of density 3.0 g/cm³ are...

Question 3

How much power is theoretically available from a mass flow of 1000 kg/s of water that falls a vertical distance of 50 m?
A) 980 kW
B) 98 kW
C) 4900 W
D) 490 kW

Accepted Answer

The theoretical power available is given by the formula P = mgh, where m is the mass flow rate, g is the acceleration due to gravity, and h is the height of fall. Substituting the given values, we get:
P = (1000 kg/s) x 9.81 m/s^2 x 50 m
P = 490,500 W = 490 kW (rounded to the nearest whole number)

Question 4

A pipe of diameter 4 cm is replaced by one of the same length but of diameter 5 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?
A) 5.1
B) 3.4
C) 2.4
D) 1.5

Accepted Answer

According to Poiseuille's law, the rate of flow of a viscous liquid through a pipe is directly proportional to the fourth power of the radius and the pressure difference, and inversely proportional to the viscosity and the length of the pipe.
Mathematically, Q = (πΔPr^4) / (8ηl), where Q is the rate of flow, ΔP is the pressure difference, r is the radius, η is the viscosity, and l is the length of the pipe.
If the diameter of the pipe is doubled, the radius becomes double, i.e., r1 = 4/2 = 2 cm, and r2 = 5/2 = 2.5 cm. 
Now, using the formula above, we can write:
Q2 / Q1 = [(2.5 / 2)^4] / [(4/2)^4] = 2.441
Therefore, the rate of flow through the pipe increases by a factor of 2.441 or approximately 2.4. 
Hence, the best answer choice is C.

Question 5

Water is sent from a fire hose at 40 m/s at an angle of 30 $\degree$ above the horizontal. What is the maximum height reached by the water?
A) 7.5 m
B) 11 m
C) 15 m
D) 20 m

Accepted Answer

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

Question 6

A fluid has a density of 1040 kg/m³. If it rises to a height of 1.8 cm in a 2.0-mm diameter capillary tube, what is the surface tension of the liquid? A) 0.046 N/m B) 0.056 N/m C) 0.092 N/m D) 0.11 N/m

Accepted Answer

The answer of A fluid has a density of 1040...

Question 7

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 15 m/s, what is the speed of the water inside the hose?
A) 0.63 m/s
B) 0.94 m/s
C) 2.5 m/s
D) also 10 m/s

Accepted Answer

We can use the equation of continuity to solve this problem:

A1V1 = A2V2

where A1 and V1 are the cross-sectional area and velocity of the water inside the hose, and A2 and V2 are the corresponding values at the nozzle opening.

We can first calculate the cross-sectional area of the hose:

A1 = πr1^2 = π(0.01 m)^2 = 3.14 x 10^-4 m^2

where r1 is the radius of the hose (which is half of its diameter).

We can then calculate the cross-sectional area of the nozzle opening:

A2 = πr2^2 = π(0.0025 m)^2 = 1.96 x 10^-5 m^2

where r2 is the radius of the nozzle opening.

We are given V2 = 15 m/s. Substituting these values into the equation of continuity, we can solve for V1:

V1 = (A2/A1) V2 = (1.96 x 10^-5 m^2 / 3.14 x 10^-4 m^2) x 15 m/s ≈ 0.94 m/s

Therefore, the speed of water inside the hose is 0.94 m/s.

Question 8

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) 1.1 m/s.
B) 2.2 m/s.
C) 4.4 m/s.
D) 8.8 m/s.

Accepted Answer

The answer of A fluid is drawn up through a...

Question 9

It takes 2.0 minutes to fill a gas tank with 60 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? (1000 liters = one cubic meter)
A) 0.27 m/s
B) 1.1 m/s
C) 1.6 m/s
D) 64 m/s

Accepted Answer

First, we need to convert the liters of gasoline to cubic meters. 
60 L = 0.06 cubic meters

Next, we can use the equation for the volume flow rate of a liquid:
Q = Av 
where Q is the volume flow rate (in cubic meters per second), A is the cross-sectional area of the nozzle (in square meters), and v is the average velocity of the liquid (in meters per second).

We know that it takes 2.0 minutes to fill the tank, so the volume flow rate is:
Q = 0.06 cubic meters / (2.0 minutes x 60 seconds/minute)
Q = 0.0005 cubic meters per second

We are given that the radius of the nozzle is 1.0 cm, which means the cross-sectional area is:
A = πr^2
A = π(0.01 m)^2
A = 0.000314 square meters

Now we can solve for the average velocity:
v = Q/A
v = (0.0005 cubic meters / second) / (0.000314 square meters)
v = 1.59 meters per second

Rounding this to one significant figure, we get an answer of:
v = 1.6 m/s

Therefore, the best answer is C, 1.6 m/s.

Question 10

A centrifuge rotates at 100 rev/s (i.e., 628 rad/s). If the test tube places the suspension at 10 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? A) 3.2 * 10³ B) 64 C) 800 D) 4.0 * 10⁴

Accepted Answer

The answer of A centrifuge rotates at 100 rev/s (i.e.,...

Question 11

Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?
A) It is at a maximum.
B) It is upwards.
C) It is downwards.
D) It is zero.

Accepted Answer

At terminal speed, the air resistance force acting on the particle is equal in magnitude and opposite in direction to the gravitational force. This means that there is no net force acting on the particle and it moves at a constant velocity. Therefore, the net force is zero.

Question 12

The fluid to which Bernoulli's equation is applied is based on what being conserved for the fluid?
A) its momentum
B) its potential energy
C) its kinetic energy
D) its total mechanical energy

Accepted Answer

Bernoulli's equation is based on the conservation of total mechanical energy for an ideal fluid, which includes the conservation of potential energy and kinetic energy.

Question 13

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 in an incompressible fluid flowing through a pipe of varying diameter. This means that the product of density, velocity, and cross-sectional area is constant at any given point in the pipe, and therefore the flow rate must also be constant. Kinetic energy, momentum, and potential energy may all vary depending on the forces acting on the fluid, but they are not conserved quantities in this scenario.

Question 14

The SI units for viscosity are N·s/m². Another commonly used unit for viscosity is the poise, where 10 poise = 1 N·s/m². The poise is a fairly large unit, and it is more common to use the centipoise. Which of the following is equal to the centipoise? A) 10^-³ N·s/m² B) 10^-² N·s/m² C) 10^-¹ N·s/m² D) 10² N·s/m²

Accepted Answer

1 centipoise = 10^-2 N·s/m²

Quiz 10: 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 15 minutes. What is the greatest terminal velocity of the particles still in suspension at that time?

Spherical particles of density 3.0 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?

How much power is theoretically available from a mass flow of 1000 kg/s of water that falls a vertical distance of 50 m?

A pipe of diameter 4 cm is replaced by one of the same length but of diameter 5 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?

Water is sent from a fire hose at 40 m/s at an angle of 30 $\degree$ above the horizontal. What is the maximum height reached by the water?

A fluid has a density of 1040 kg/m³. If it rises to a height of 1.8 cm in a 2.0-mm diameter capillary tube, what is the surface tension of the liquid?

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 15 m/s, what is the speed of the water inside the hose?

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:

It takes 2.0 minutes to fill a gas tank with 60 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? (1000 liters = one cubic meter)

A centrifuge rotates at 100 rev/s (i.e., 628 rad/s) . If the test tube places the suspension at 10 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?

The fluid to which Bernoulli's equation is applied is based on what being conserved for the fluid?

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?

The SI units for viscosity are N·s/m². Another commonly used unit for viscosity is the poise, where 10 poise = 1 N·s/m². The poise is a fairly large unit, and it is more common to use the centipoise. Which of the following is equal to the centipoise?