Question 1

Consider a viscous fluid flowing through a cylindrical tube. If we reduce the area of the cross-section by half, how will the flow rate change?

Accepted Answer

The flow rate in a cylindrical tube is inversely proportional to the viscosity and directly proportional to the fourth power of the radius (according to the Hagen-Poiseuille equation). Halving the cross-sectional area reduces the radius by a factor of $\sqrt{2}$, and thus the flow rate decreases by $2^4 = 16$ times. However, given the options, the closest applicable effect is a significant decrease, which is best represented by option D, indicating a substantial decrease in flow rate, albeit the exact factor might be misstated without the option that precisely matches the $16$ times reduction.

Question 2

The continuity equation (ÄV/Ät = const) is a consequence of conservation of which of the following aspects?

Accepted Answer

The continuity equation is a consequence of the conservation of mass, stating that the mass of a fluid remains constant as it flows from one point to another.

Question 3

How will the force that is required to slide microscope slides past each other change if we reduce the separation between slides by 100 times, while retaining the velocity?

Accepted Answer

The force required to slide microscope slides past each other is directly proportional to the viscosity of the fluid between them and the velocity, and inversely proportional to the separation between the slides. Reducing the separation by 100 times would increase the force required by the same factor, according to the formula F = (ηA*v)/d, where η is the viscosity, A is the area, v is the velocity, and d is the separation distance.

Question 4

Which of the following is a property of an ideal fluid?

Accepted Answer

An ideal fluid is characterized by incompressibility, meaning its volume does not change under pressure. This is a key assumption in many theoretical fluid dynamics models to simplify the mathematics involved.

Question 5

A fluid flows at a rate of 30 L per minute through a pipe that has a cross-sectional radius of 2 cm. How will the flow change in the part of the pipe where the radius is constricted to half of its value?

Accepted Answer

The flow rate of a fluid (volume per unit time) remains constant throughout a pipe system as long as the system is closed and there are no leaks, according to the principle of conservation of mass. This principle is embodied in the equation of continuity for fluid flow.

Question 6

Which quantity is conserved when Ohm's law is applied to a blood vessel that has variable resistance along its length?

Accepted Answer

When Ohm's law is applied to a blood vessel, the flow rate (volume per unit time) is conserved even if the resistance varies along the length of the vessel. This is analogous to electrical current being conserved in a circuit regardless of variations in resistance.

Question 7

Blood flows through an artery that has a narrowing of its diameter by 15% due to clogging. How does the speed of blood change in the area with the constricted cross-section?

Accepted Answer

The speed of blood increases in the narrowed section because the volume flow rate must remain constant throughout the artery. According to the principle of continuity, if the cross-sectional area decreases, the velocity must increase to maintain a constant flow rate. A 15% decrease in diameter leads to a decrease in the cross-sectional area, necessitating an increase in speed. The exact factor of increase depends on the specifics of the narrowing, but the principle dictates that the speed must increase, not decrease or stay the same.

Question 8

Bernoulli's equation is a consequence of conservation of which of the following?

Accepted Answer

Bernoulli's equation is derived from the principle of conservation of energy, specifically for fluid flow. It relates the pressure, velocity, and elevation of a fluid in motion, showing that the total mechanical energy of the fluid parcel remains constant.

Question 9

A pipe is delivering water at a rate of 25 L per minute. The diameter of the pipe opening is 2.0 cm. What is the speed of water flow?

Accepted Answer

The speed of water flow can be calculated using the formula for the volume flow rate, $Q = A \cdot v$, where $Q$ is the volume flow rate, $A$ is the cross-sectional area of the pipe, and $v$ is the speed of the water. Given $Q = 25$ L/min, which is $0.025$ m³/min or $\frac{0.025}{60}$ m³/s (since there are 60 seconds in a minute), and the diameter of the pipe is $2.0$ cm or $0.02$ m, the area $A = \pi r^2 = \pi (0.01)^2 = 3.14 \times 10^{-4}$ m². Solving for $v$, $v = \frac{Q}{A} = \frac{0.025/60}{3.14 \times 10^{-4}} \approx 1.3$ m/s.

Question 10

Which of these statements describes a flow rate?

Accepted Answer

Flow rate is the change of volume with time.

Question 11

The human body prioritizes its oxygen supply via blood based on the relevance of the organ and metabolic demand. What is the correct order of priorities of these selected organs, ranked from the highest to the lowest?

Accepted Answer

The brain and heart have the highest priority for oxygen supply due to their critical functions and high metabolic demands. The kidneys and liver follow, with the kidneys having a slightly higher priority than the liver.

Question 12

One of the terms in Bernoulli's equation is ½ ñv². Which of these quantities does it represent?

Accepted Answer

The term ½ ñv^2 represents kinetic energy per unit volume in Bernoulli's equation, where ñ is the fluid density and v is the fluid velocity.

Question 13

Corn syrup flows through a tube with a radius of 2 cm and a length of 2 m, at a speed of 0.4 m/s. What is the pressure difference in the tube? (Viscosity of syrup is ç = 1.38 Pa s.)

Accepted Answer

The pressure difference in the tube can be calculated using Poiseuille's law, which is given by $\Delta P = \frac{8 \mu L v}{\pi r^4}$, where $\Delta P$ is the pressure difference, $\mu$ is the viscosity of the fluid, $L$ is the length of the tube, $v$ is the speed of the fluid, and $r$ is the radius of the tube. Substituting the given values: $\Delta P = \frac{8 \times 1.38 \times 2 \times 0.4}{\pi \times (0.02)^4}$, we find that the pressure difference is approximately 22 kPa.

Question 14

Poiseuille's law for flow of a fluid through a tube relates flow rate, drop of pressure over the length of the tube, velocity of the fluid, and radius of the tube. In which of the following situations would there be no pressure drop?

Accepted Answer

Poiseuille's law indicates that the pressure drop across a tube is directly proportional to the viscosity of the fluid. If the viscosity is zero, indicating an ideal fluid with no internal friction, there would be no pressure drop across the tube.

Question 15

A fluid is flowing through a tube with a diameter of 4 mm, a length of 40 cm, at a speed of 0.7 m/s. The pressure drop is 950 Pa. What is the viscosity of the fluid?

Accepted Answer

The answer of A fluid is flowing through a tube...

Question 16

Water flows at 3 m/s through a horizontal pipe where the pressure is 2.3 × 10⁵ Pa. Where the pipe constricts to a quarter of its original area, what is the pressure?

Accepted Answer

This problem can be solved using Bernoulli's equation, which in one of its forms states that for an incompressible fluid flowing through a pipe, the sum of the pressure energy, kinetic energy per unit volume, and potential energy per unit volume remains constant. Since the pipe is horizontal, changes in potential energy can be ignored. The equation simplifies to $P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$, where $P_1$ and $P_2$ are the pressures at points 1 and 2, $v_1$ and $v_2$ are the velocities at points 1 and 2, and $\rho$ is the density of the fluid. Given that the area decreases to a quarter of its original size, the velocity at point 2 ($v_2$) will be four times $v_1$ due to the continuity equation $A_1v_1 = A_2v_2$, leading to $v_2 = 4v_1 = 12 \, \text{m/s}$. Substituting the given values and solving for $P_2$ will show that the pressure decreases due to the increase in kinetic energy, resulting in the correct answer being 1.6 × 10^5 Pa.

Question 17

If two liquids with different viscosities flow through tubes with identical parameters, how do their flow rates differ?

Accepted Answer

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. A higher viscosity means the fluid is "thicker" and flows more slowly under the same conditions, leading to a lower flow rate compared to a fluid with lower viscosity.

Question 18

The fluid flow rate is 1.1 L per minute, and the tube has a diameter of 4 mm and a length of 10 cm. What is the viscosity of the fluid if the pressure drops 5.3 Pa over the length of the tube?

Accepted Answer

The answer of The fluid flow rate is 1.1 L...

Question 19

Blood flows with a velocity of 0.22 m/s through an artery that has a narrowing of the diameter by 15% due to clogging. How does the pressure of the blood change in the area that has the constricted cross-section? The density of blood is ñ = 1060 kg/m³.

Accepted Answer

The answer of Blood flows with a velocity of 0.22...

Question 20

Water flows through a pipe that widens out to double its original diameter. How does the speed of water change in the area with the wider cross-section?

Accepted Answer

According to the principle of continuity for incompressible fluids, the flow rate must remain constant. When the diameter doubles, the cross-sectional area increases by four times (since area is proportional to the square of the diameter). Therefore, the speed of the water decreases by four times to maintain the same flow rate.

Quiz 12: Fluid Flow