Question 1

How much air must be pushed downward at 40.0 m/s to keep an 830-kg helicopter aloft?

Accepted Answer

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

Question 2

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

According to the Poiseuille's law, the rate of flow through a pipe is proportional to the fourth power of its radius. Hence, the rate of flow through the new pipe with twice the radius will be 2^4=16 times that of the old pipe. Thus, the answer is D) 16.

Question 3

In addition to its weight,what force is needed to lift a wire ring of radius 2.0 cm from the surface of blood plasma? The surface tension of blood plasma is 7.3 × 10¯²N/m.

Accepted Answer

The force needed to lift the wire ring is calculated using the formula F = 2πrγ, where r is the radius and γ is the surface tension. Substituting the given values, F = 2π(0.02 m)(7.3 × 10¯² N/m) = 1.8 × 10¯² N.

Question 4

A fluid is drawn up through a tube as shown in the figure.If the height difference from the top of the tank to the bottom of the siphon is H = 1.40 m,then what is the outflow speed? Assume the pressure is the same at the top of the tank and at the siphon outlet. 
​

Accepted Answer

The outflow speed can be determined using Bernoulli's equation:
P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2
where P is the pressure, ρ is the density, v is the velocity, g is the acceleration due to gravity, and h is the height.

Assuming the pressure is the same at the top of the tank and at the siphon outlet (P1 = P2), and the velocity at the top of the tank is negligible (v1 = 0), we can simplify the equation to:
(1/2)ρv2^2 + ρgh2 = 0

Solving for v2, we get:
v2 = sqrt(2gh2) = sqrt(2gH) = 5.24 m/s

Therefore, the answer is C.

Question 5

Spherical particles of density 1.8 g/cm³ are shaken in a container of water (viscosity = 1.0 × 10−³ N⋅s/m³).The water is 9.0 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 settling velocity of a particle in a fluid can be calculated using Stoke's law:

v = (2/9) * (r^2) * (p-p0) * g / η

Where:
v = terminal settling velocity
r = radius of particle
p = density of particle
p0 = density of fluid
g = acceleration due to gravity
η = viscosity of fluid

For spherical particles in water, the maximum size that will remain suspended can be calculated as follows:

v = 0.0254 m / 1800 kg/m^3 * 9.8 m/s^2 / (1.0 × 10^-3 N⋅s/m^2) = 1.49 × 10^-5 m/s

After 30 minutes, the maximum distance a particle can travel while still remaining suspended is:

d = v * t = 1.49 × 10^-5 m/s * 1800 s = 0.0268 m

The maximum radius of a particle that can travel this distance is:

r = d / 2 = 0.0268 m / 2 = 0.0134 m = 1.34 × 10^-5 m

Therefore, the largest particle that can remain suspended has a radius of approximately 5.4E-6 m. The closest choice is C.

Question 6

A centrifuge rotates at 100 rev/s (i.e. ,628 rad/s).If the test tube places the suspension at 8.00 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 force acting on a particle in a centrifuge is given by $F = m\omega^2r$, where $m$ is the mass of the particle, $\omega$ is the angular velocity in rad/s, and $r$ is the radius from the axis of rotation. The force due to gravity acting on the same particle is $F_g = mg$, where $g$ is the acceleration due to gravity ($9.8 m/s^2$). The factor by which the terminal speeds are increased is given by the ratio of the centrifugal force to the gravitational force, which is $\frac{m\omega^2r}{mg} = \frac{\omega^2r}{g}$.Given $\omega = 628 rad/s$ and $r = 8.00 cm = 0.08 m$, we can calculate this factor as follows:$$\frac{\omega^2r}{g} = \frac{(628)^2 \times 0.08}{9.8} \approx 3.2 \times 10^3$$Therefore, the terminal speeds of the settling particles are increased by a factor of approximately 3200 compared to sedimentation caused by gravity.

Question 7

Water is sent from a fire hose at 34.5 m/s at an angle of 30.0° above the horizontal.What is the maximum height reached by the water,assuming the fire hose is level with the ground?

Accepted Answer

We can use the equation for maximum height:

H = (v^2 sin^2θ)/(2g)

where v is the initial velocity (34.5 m/s), θ is the angle of the hose (30.0°), and g is the acceleration due to gravity (9.81 m/s^2).

Plugging in the values, we get:

H = (34.5^2 sin^2(30°))/(2*9.81) = 15.2 m

Therefore, the maximum height reached by the water is 15.2 m, which is choice B.

Question 8

A fluid has a density of 1 040 kg/m³.If it rises to a height of 1.60 cm in a 1.50-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

Accepted Answer

The surface tension ($\gamma$) of the liquid can be calculated using the formula for capillary rise: $\gamma = \frac{\rho g h r}{2\cos(\theta)}$, where $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity, $h$ is the height the fluid rises in the capillary, $r$ is the radius of the capillary tube, and $\theta$ is the contact angle. Given $\rho = 1040 \, \text{kg/m}^3$, $g = 9.8 \, \text{m/s}^2$, $h = 0.016 \, \text{m}$ (converted from 1.60 cm), $r = 0.00075 \, \text{m}$ (half of the diameter, which is 1.50 mm or 0.0015 m), and $\theta = 0$ (which makes $\cos(\theta) = 1$), substituting these values into the formula gives $\gamma = 0.0612 \, \text{N/m}$.

Question 9

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?

Accepted Answer

1 centipoise = 10^-3 N·s/m²

Question 10

How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls a vertical distance of 120 m?

Accepted Answer

The theoretical power available from a mass flow of water that falls a vertical distance can be calculated using the formula:

Power = (mass flow rate) x (gravity) x (height)

where gravity = 9.81 m/s^2

Substituting the given values in the formula, we get:

Power = 1000 kg/s x 9.81 m/s^2 x 120 m
Power = 1,176,960 W = 1.18E+6 kW

Therefore, the correct answer is A) 1.18E+6 kW.

Question 11

A jet of water flowing from a hose at 18 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 applied by the water to the wall can be calculated using the formula for the rate of change of momentum, which is $F = \Delta p / \Delta t$, where $F$ is the force, $\Delta p$ is the change in momentum, and $\Delta t$ is the change in time. Since the water stops upon hitting the wall, its final velocity is 0 m/s, and the change in velocity is equal to its initial velocity (18 m/s). The mass flow rate is 2.0 kg/s, which means 2.0 kg of water hits the wall every second. The change in momentum per second ($\Delta p / \Delta t$) is thus $2.0 \, \text{kg/s} \times 18 \, \text{m/s} = 36 \, \text{N}$, indicating the force applied is 36 N.

Question 12

In order to overcome a surface tension of a fluid,a force of 1.35 × 10−² N is required to lift a wire ring of circumference 13.0 cm.What is the surface tension of the fluid?

Accepted Answer

Surface tension = Force required to lift the ring / Circumference of the ring= 1.35 × 10−² N / 13.0 cm= 0.052 N/m

Question 13

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 9.0 cm deep and is allowed to stand for 25 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 14

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 streamlined. This is because the Reynolds number (Re) for this flow is less than 2000, which is the critical value for the transition from laminar to turbulent flow. The Reynolds number can be calculated as Re = (ρvD)/μ, where ρ is the density of water, v is the flow velocity, D is the diameter of the pipe (2 cm), and μ is the viscosity of water. Plugging in the values gives Re = 90, which is well below the critical value of 2000, indicating a streamlined flow.

Question 15

Air pressure is 1.00 × 10⁵ N/m²,air density is 1.30 kg/m³,and the density of soft drinks is 1.00 × 10³ kg/m³.If one blows carefully across the top of a straw sticking up 0.10 m from the liquid in a soft drink can,it is possible to make the soft drink rise half way up the straw and stay there.How fast must the air be blown across the top of the straw?

Accepted Answer

Using Bernoulli's equation, the speed of air needed to create a pressure difference that supports the liquid column is approximately 27 m/s.

Question 16

The flow rate of blood through the average human aorta,of radius 0.95 cm,is about 90 cm³/s.What is the speed of the blood flow through the aorta?

Accepted Answer

The answer of The flow rate of blood through the...

Question 17

A water pipe with inner radius r₁ is connected to a junction with two equal-diameter pipes.Water flows through each of the two pipes with a speed of v.If the diameter of each of the two pipes is ¼ the diameter of the single pipe,what is the flow rate in the single pipe?

Accepted Answer

The flow rate is proportional to the cross-sectional area of the pipe. The cross-sectional area of the single pipe is 4 times the cross-sectional area of each of the two pipes. Therefore, the flow rate in the single pipe is 4 times the flow rate in each of the two pipes.

Question 18

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

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 19

When an artery gets a constricted region due to plaque,how does the pressure in this region compare to the pressure in an unconstricted region adjacent?

Accepted Answer

According to Bernoulli's principle, when the velocity of a fluid increases, its pressure decreases. In the constricted region of an artery, blood moves at a higher speed compared to the unconstricted region, leading to a decrease in pressure.

Question 20

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...

Quiz 9: Fluids and Solids

How much air must be pushed downward at 40.0 m/s to keep an 830-kg helicopter aloft?

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?

In addition to its weight,what force is needed to lift a wire ring of radius 2.0 cm from the surface of blood plasma? The surface tension of blood plasma is 7.3 × 10¯²N/m.

A fluid is drawn up through a tube as shown in the figure.If the height difference from the top of the tank to the bottom of the siphon is H = 1.40 m,then what is the outflow speed? Assume the pressure is the same at the top of the tank and at the siphon outlet.

Spherical particles of density 1.8 g/cm³ are shaken in a container of water (viscosity = 1.0 × 10−³ N⋅s/m³) .The water is 9.0 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 centrifuge rotates at 100 rev/s (i.e. ,628 rad/s) .If the test tube places the suspension at 8.00 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?

Water is sent from a fire hose at 34.5 m/s at an angle of 30.0° above the horizontal.What is the maximum height reached by the water,assuming the fire hose is level with the ground?

A fluid has a density of 1 040 kg/m³.If it rises to a height of 1.60 cm in a 1.50-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

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?

How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls a vertical distance of 120 m?

A jet of water flowing from a hose at 18 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?

In order to overcome a surface tension of a fluid,a force of 1.35 × 10−² N is required to lift a wire ring of circumference 13.0 cm.What is the surface tension of the fluid?

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 9.0 cm deep and is allowed to stand for 25 minutes.What is the greatest terminal velocity of the particles still in suspension at that time?

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.

The flow rate of blood through the average human aorta,of radius 0.95 cm,is about 90 cm³/s.What is the speed of the blood flow through the aorta?

A water pipe with inner radius r₁ is connected to a junction with two equal-diameter pipes.Water flows through each of the two pipes with a speed of v.If the diameter of each of the two pipes is ¼ the diameter of the single pipe,what is the flow rate in the single pipe?

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

When an artery gets a constricted region due to plaque,how does the pressure in this region compare to the pressure in an unconstricted region adjacent?

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

Quiz 9: Fluids and Solids

How much air must be pushed downward at 40.0 m/s to keep an 830-kg helicopter aloft?

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?

In addition to its weight,what force is needed to lift a wire ring of radius 2.0 cm from the surface of blood plasma? The surface tension of blood plasma is 7.3 × 10¯2 N/m.

A fluid is drawn up through a tube as shown in the figure.If the height difference from the top of the tank to the bottom of the siphon is H = 1.40 m,then what is the outflow speed? Assume the pressure is the same at the top of the tank and at the siphon outlet. ​

Spherical particles of density 1.8 g/cm3 are shaken in a container of water (viscosity = 1.0 × 10−3 N⋅s/m3) .The water is 9.0 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 centrifuge rotates at 100 rev/s (i.e. ,628 rad/s) .If the test tube places the suspension at 8.00 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?

Water is sent from a fire hose at 34.5 m/s at an angle of 30.0° above the horizontal.What is the maximum height reached by the water,assuming the fire hose is level with the ground?

A fluid has a density of 1 040 kg/m3.If it rises to a height of 1.60 cm in a 1.50-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

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?

How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls a vertical distance of 120 m?

A jet of water flowing from a hose at 18 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?

In order to overcome a surface tension of a fluid,a force of 1.35 × 10−2 N is required to lift a wire ring of circumference 13.0 cm.What is the surface tension of the fluid?

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 9.0 cm deep and is allowed to stand for 25 minutes.What is the greatest terminal velocity of the particles still in suspension at that time?​

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.

The flow rate of blood through the average human aorta,of radius 0.95 cm,is about 90 cm3/s.What is the speed of the blood flow through the aorta?

​A water pipe with inner radius r1 is connected to a junction with two equal-diameter pipes.Water flows through each of the two pipes with a speed of v.If the diameter of each of the two pipes is ¼ the diameter of the single pipe,what is the flow rate in the single pipe?

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

When an artery gets a constricted region due to plaque,how does the pressure in this region compare to the pressure in an unconstricted region adjacent?

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

In addition to its weight,what force is needed to lift a wire ring of radius 2.0 cm from the surface of blood plasma? The surface tension of blood plasma is 7.3 × 10¯²N/m.

A fluid is drawn up through a tube as shown in the figure.If the height difference from the top of the tank to the bottom of the siphon is H = 1.40 m,then what is the outflow speed? Assume the pressure is the same at the top of the tank and at the siphon outlet.

Spherical particles of density 1.8 g/cm³ are shaken in a container of water (viscosity = 1.0 × 10−³ N⋅s/m³) .The water is 9.0 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 1.60 cm in a 1.50-mm diameter capillary tube,what is the surface tension of the liquid? Assume a contact angle of zero.

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?

In order to overcome a surface tension of a fluid,a force of 1.35 × 10−² N is required to lift a wire ring of circumference 13.0 cm.What is the surface tension of the fluid?

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 9.0 cm deep and is allowed to stand for 25 minutes.What is the greatest terminal velocity of the particles still in suspension at that time?

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.

The flow rate of blood through the average human aorta,of radius 0.95 cm,is about 90 cm³/s.What is the speed of the blood flow through the aorta?

A water pipe with inner radius r₁ is connected to a junction with two equal-diameter pipes.Water flows through each of the two pipes with a speed of v.If the diameter of each of the two pipes is ¼ the diameter of the single pipe,what is the flow rate in the single pipe?