Question 1

Viscosity: Suppose that the build-up of fatty tissue on the wall of an artery decreased the radius by 10%. By what percent would the arterial pressure difference produced by the heart have to be increased to maintain a constant blood flow?

Accepted Answer

The answer of Viscosity: Suppose that the build-up of fatty...

Question 2

Viscosity: A flat horizontal plate of area 400 cm² is dragged over a 0.20 cm thick layer of oil at a speed of 30.0 cm/s. The oil is resting on a fixed horizontal surface. It takes a force 1.20 N applied to the plate to sustain this speed. What is the viscosity of the oil?

Accepted Answer

The viscosity η can be calculated using the formula η = (F * d) / (A * v), where F is the force, d is the thickness of the oil layer, A is the area, and v is the velocity. Substituting the given values: η = (1.20 N * 0.002 m) / (0.04 m² * 0.30 m/s) = 0.200 kg/m ∙ s.

Question 3

Bernoulli's principle: In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m³?

Accepted Answer

The answer of Bernoulli's principle: In a section of horizontal...

Question 4

Bernoulli's principle: Water flows in the horizontal pipe shown in the figure. At point A the area is 25.0 cm² and the speed of the water is 2.00 m/s. At B the area is 16.0 cm². The fluid in the manometer is mercury, which has a density of 13,600 kg/m³. We can treat water as an ideal fluid having a density of 1000 kg/m³. What is the manometer reading h?

Accepted Answer

Applying Bernoulli's principle between points A and B, we have:

P + 1/2ρv² + ρgh = constant

Since the pipe is horizontal, we can neglect the term involving the height difference (h) between A and B. Also, we will assume that the pressure at A and B is atmospheric pressure (since the problem does not provide any other information). Thus, we have:

1/2ρAvA² = 1/2ρBvB²

Solving for vB, we get:

vB = √(AvA²/B)

Substituting the given values, we get:

vB = 2.50 m/s

Now, we can apply Bernoulli's principle again between points B and C (the top of the mercury column in the right arm of the manometer).

P + 1/2ρv² + ρgh = constant

Since the fluid in the manometer is mercury, we need to use its density to calculate the pressure difference between points B and C. Thus, we have:

P + 1/2ρBvB² = P + ρHggh

Solving for h, we get:

h = vB²/(2gρHg)

Substituting the given values, we get:

h = 0.0216 m = 2.16 cm

Therefore, the answer is D.

Question 5

Bernoulli's principle: A level pipe contains a nonviscous, incompressible fluid with a density 1200 kg/m³ that is flowing steadily. At one position within the pipe, the pressure is 300 kPa and the speed of the flow is 20.0 m/s. At another position, the pressure is 200 kPa. What is the speed of the flow at this second position?

Accepted Answer

According to Bernoulli's principle, the total energy (sum of kinetic energy, potential energy, and pressure energy) of a nonviscous, incompressible fluid is conserved along a streamline. Mathematically, this principle can be expressed as:

ρgh + 1/2 ρv^2 + P = constant

where ρ is the density of the fluid, g is the acceleration due to gravity, h is the height above a reference point, v is the speed of the flow, and P is the pressure of the fluid.

At the first position, we know that P = 300 kPa and v = 20.0 m/s. Let's assume that the height is the same at both positions (i.e. h1 = h2). Then we can write:

1/2 ρv1^2 + P1 = 1/2 ρv2^2 + P2

Substituting the given values, we get:

1/2 (1200 kg/m^3)(20.0 m/s)^2 + 300 kPa = 1/2 (1200 kg/m^3)v2^2 + 200 kPa

Simplifying this equation, we can solve for v2:

v2 = sqrt[(2(1/2 (1200 kg/m^3)(20.0 m/s)^2 + 300 kPa - 200 kPa))/1200 kg/m^3] = 23.8 m/s

Therefore, the answer is (D) 23.8 m/s.

Question 6

Viscosity: Motor oil, with a viscosity of 0.250 N ∙ s/m², is flowing through a tube that has a radius of 5.00 mm and is 25.0 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per second?

Accepted Answer

Using Poiseuille's Law, we can calculate the volume flow rate:
$V = \frac{\pi r^4 \Delta P}{8\eta L}$
Plugging in the given values, we get:
$V = \frac{\pi (0.005	ext{ m})^4 (300,000	ext{ Pa})}{8(0.250	ext{ N}\cdot	ext{s/m}^2)(0.25	ext{ m})} \approx 0.00118	ext{ m}^3/	ext{s}$
Therefore, the volume of oil flowing through the tube per second is approximately 0.00118 m³/s, which corresponds to choice C.

Question 7

Bernoulli's principle: Water flows in the horizontal pipe shown in the figure. At A the diameter is 5.00 cm and at B the diameter is 4.00 cm The fluid in the manometer is mercury, which has a density of 13,600 kg/m³. The manometer reading h is 4.40 cm. We can treat water as an ideal fluid having a density of 1000 kg/m³. What volume of water is flowing through the pipe per second?

Accepted Answer

The answer of Bernoulli's principle: Water flows in the horizontal...

Question 8

Bernoulli's principle: Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5.25 kg/m³ and a speed of 1.20 m/s. The interior diameter of the rocket is 15.0 cm. At the nozzle exit, the diameter is 2.50 cm and the density is 1.29 kg/m³. What is the speed of the air when it leaves the nozzle?

Accepted Answer

The answer of Bernoulli's principle: Air is flowing through a...

Question 9

Bernoulli's principle: A large cylindrical water tank is mounted on a platform with its central axis vertical. The water level is 3.75 m above the base of the tank, and base is 6.50 m above the ground. A small hole 2.22 mm in diameter has formed in the base of the tank. Both the hole and the top of the tank are open to the air. We can ignore air resistance and treat water as an ideal fluid with a density of 1000 kg/m³. (a) How many cubic meters of water per second is this tank losing? (b) How fast is the water from the hole moving just as it reaches the ground?

Accepted Answer

The answer of Bernoulli's principle: A large cylindrical water tank...

Question 10

Bernoulli's principle: A horizontal tube consists of a pipe that narrows to a 2.0-cm-diameter throat. In the pipe, the water pressure is twice atmospheric pressure and the water flows with a speed of What is the pressure in the throat, assuming that the water behaves like an ideal fluid? The density of water is 1000 kg/m³, and atmospheric pressure is 1.01 × 10⁵ Pa.

Accepted Answer

The answer of Bernoulli's principle: A horizontal tube consists of...

Question 11

Viscosity: Glycerin, with a viscosity of 1.50 N ∙ s/m², is flowing with an average speed of 1.20 m/s through a tube that has a radius of 5.00 mm and is 25.0 cm long. What is the drop in pressure between the ends of the tube?

Accepted Answer

The drop in pressure can be calculated using Poiseuille's law: ΔP = 8μLv / πr^4, where ΔP is the pressure drop, μ is the viscosity, L is the length of the tube, v is the average speed, and r is the radius of the tube. Substituting the given values (μ = 1.50 N∙s/m^2, L = 0.25 m, v = 1.20 m/s, r = 0.005 m), we find ΔP = 8 * 1.50 * 0.25 * 1.20 / (π * (0.005)^4) = 144 kPa.

Question 12

Bernoulli's principle: A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe, as shown in the figure. The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream. The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s. The density of the air is 1.29 kg/m³, and the density of the paint is 1200 kg/m³. We can treat the air and paint as incompressible ideal fluids. What is the maximum diameter of the constriction that will allow the sprayer to operate?

Accepted Answer

The answer of Bernoulli's principle: A paint sprayer pumps air...

Question 13

Bernoulli's principle: Incompressible water flows out of a large reservoir through a pipe that opens to the atmosphere 5.70 m below the level of the water in the reservoir. What is the speed of the water as it comes out of the pipe?

Accepted Answer

According to Bernoulli's principle, the total energy of a fluid is conserved along a streamline. This means that the sum of the potential energy, kinetic energy, and pressure energy must remain constant.

At the surface of the reservoir, the water has only potential energy given by:

$PE = mgh$

where $m$ is the mass of the water, $g$ is the acceleration due to gravity, and $h$ is the height of the water above the opening of the pipe.

At the exit of the pipe, the water has only kinetic energy given by:

$KE = \frac{1}{2}mv^2$

where $v$ is the speed of the water.

Since there is no change in pressure energy, we can set the potential energy at the surface of the reservoir equal to the kinetic energy at the exit of the pipe:

$mgh = \frac{1}{2}mv^2$

Simplifying this expression gives:

$v = \sqrt{2gh}$

Plugging in the given values gives:

$v = \sqrt{2(9.81~m/s^2)(5.70~m)} = \boxed{10.6~m/s}$

Question 14

Bernoulli's principle: Consider a very small hole in the bottom of a tank  in diameter filled with water to a height of  Find the speed at which the water exits the tank through the hole.

Accepted Answer

The answer of Bernoulli's principle: Consider a very small hole...

Quiz 12: Fluid Mechanics

Viscosity: Suppose that the build-up of fatty tissue on the wall of an artery decreased the radius by 10%. By what percent would the arterial pressure difference produced by the heart have to be increased to maintain a constant blood flow?

Viscosity: A flat horizontal plate of area 400 cm2 is dragged over a 0.20 cm thick layer of oil at a speed of 30.0 cm/s. The oil is resting on a fixed horizontal surface. It takes a force 1.20 N applied to the plate to sustain this speed. What is the viscosity of the oil?

Bernoulli's principle: In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m3?

Viscosity: Motor oil, with a viscosity of 0.250 N ∙ s/m2, is flowing through a tube that has a radius of 5.00 mm and is 25.0 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per second?

Viscosity: Glycerin, with a viscosity of 1.50 N ∙ s/m2, is flowing with an average speed of 1.20 m/s through a tube that has a radius of 5.00 mm and is 25.0 cm long. What is the drop in pressure between the ends of the tube?

Bernoulli's principle: Incompressible water flows out of a large reservoir through a pipe that opens to the atmosphere 5.70 m below the level of the water in the reservoir. What is the speed of the water as it comes out of the pipe?

Bernoulli's principle: Consider a very small hole in the bottom of a tank in diameter filled with water to a height of Find the speed at which the water exits the tank through the hole.

Viscosity: A flat horizontal plate of area 400 cm² is dragged over a 0.20 cm thick layer of oil at a speed of 30.0 cm/s. The oil is resting on a fixed horizontal surface. It takes a force 1.20 N applied to the plate to sustain this speed. What is the viscosity of the oil?

Bernoulli's principle: In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m³?

Viscosity: Motor oil, with a viscosity of 0.250 N ∙ s/m², is flowing through a tube that has a radius of 5.00 mm and is 25.0 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per second?

Viscosity: Glycerin, with a viscosity of 1.50 N ∙ s/m², is flowing with an average speed of 1.20 m/s through a tube that has a radius of 5.00 mm and is 25.0 cm long. What is the drop in pressure between the ends of the tube?