Question 1

Two identical fish, both at sea level, float in two identical aquariums with identical quantities of water. Fish A is in Alaska, so it weighs more than fish B at the equator, since g is larger at sea level in Alaska. Which statement is correct?

Accepted Answer

The buoyant force on an object is determined by the volume of water it displaces, which is directly related to its volume, not its weight. Since the fish are identical and in identical quantities of water, they displace the same quantity of water regardless of the gravitational differences at their locations.

Question 2

A hose has been clamped so that the area at the clamp is only one quarter the area of the rest of the hose. When we ignore the viscosity of water, the ratio of the volume of water delivered per unit time when the clamp is on to the volume of water delivered per unit time without the clamp is

Accepted Answer

When the hose is clamped, the volume of water that can flow through the hose is reduced to one quarter. However, the speed of the water flowing through the hose remains the same (when ignoring viscosity). Therefore, the volume of water delivered per unit time both with and without the clamp will be the same. Thus, the ratio of the volume of water delivered per unit time when the clamp is on to the volume of water delivered per unit time without the clamp is 1:1 or simply 1. Therefore, the answer is E.

Question 3

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

Accepted Answer

The theoretical power available from a mass flow of water can be calculated using the formula:
P = mgh
where P is power, m is the mass flow rate, g is the acceleration due to gravity (9.81 m/s^2), and h is the vertical distance the water falls.
Plugging in the given values, we get:
P = (1000 kg/s) x (9.81 m/s^2) x (100 m)
P = 981,000 W or 981 kW (rounded to nearest thousand)
Therefore, the answer is A) 980 kW, as it is the closest to the calculated value.

Question 4

The figure below shows a container filled with water to the height shown. When we compare the pressure at A to the pressure at B, we find that

Accepted Answer

The answer of The figure below shows a container filled...

Question 5

An empty spice bottle has an inner volume of 1.31 × 10−⁴ m³. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10−⁴ m³ of water when fully submerged. What fraction of the total volume of the bottle will be beneath the surface when it is placed in a tank of water?

Accepted Answer

The fraction of the volume submerged is the volume of water displaced divided by the inner volume of the bottle: (1.31 × 10^-4 m³) / (1.63 × 10^-4 m³) = 0.69.

Question 6

A police crime lab is trying to determine whether someone was murdered or died as a result of an accident. He was struck in the temple by a 4.20 kg sculpture that is alleged to have fallen off a bookcase. The sculpture presumably fell a distance of 1.43 m and the corner that struck him had an area of 0.250 cm². If the time for the sculpture to stop was 1.00 ms, the pressure on his temple, in N/m², was

Accepted Answer

The answer of A police crime lab is trying to...

Question 7

A waiter in a restaurant fills a pitcher full of water and ice so that water would spill out if any more were added. As the ice starts to melt

Accepted Answer

When ice melts in water, it converts to liquid water without changing the overall water level in the pitcher. This is because the volume of water produced by the melting ice exactly replaces the volume previously displaced by the ice. The principle of buoyancy dictates that the amount of water displaced by the ice is equal to the weight of the ice. When the ice melts, it turns into the same amount of water it had displaced, keeping the water level constant.

Question 8

A wood block is placed on top of the ice in a large bowl half full of ice. The bowl is then filled to the brim with water, with the wood block riding on top of the ice. As the ice melts,

Accepted Answer

When ice melts, it turns into water which occupies the same volume. Therefore, the total volume of the ice and water remain the same. Since the wood block is placed on top of the ice and not submerged, it does not displace any water. Hence, the water level does not change.

Question 9

A venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (ρ = 1.2 kg/m³.)

Accepted Answer

We can use the Bernoulli's equation which states:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

where P1 and v1 are the pressure and velocity at the wider section and P2 and v2 are the pressure and velocity at the constricted section.

Since the venturi tube is horizontal, we can assume that the height difference between the two sections is negligible and can be ignored. Therefore, the Bernoulli's equation can be simplified as:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

Rearranging the equation, we get:

P2 - P1 = (1/2)ρ(v1^2 - v2^2)

Substituting the given values, we have:

P2 - P1 = (1/2)(1.2 kg/m3)(3.0 m/s)^2((2.0 cm/2)^2 - (1.0 cm/2)^2)/100 cm/m = 0.81 kPa

Converting kPa to Pa, we get the answer:

P2 - P1 = 81 Pa

Therefore, the correct choice is E.

Question 10

Water is sent from a firehose at 30.0 m/s at an angle of 30.0° above the horizontal. What is the maximum height reached by the water?

Accepted Answer

The vertical component of the velocity is $ v_{0y} = 30.0 \, \text{m/s} \times \sin(30.0^\circ) = 15.0 \, \text{m/s} $. Using the formula for maximum height $ h = \frac{v_{0y}^2}{2g} $, where $ g = 9.8 \, \text{m/s}^2 $, we get $ h = \frac{(15.0)^2}{2 \times 9.8} = 11.5 \, \text{m} $.

Question 11

The siphon shown is used to transfer liquid from a higher level to a lower level. If the fluid is drawn up and is continuous through the tube, determine the velocity of flow of gasoline if the vertical distance from the liquid surface to the outlet is 1.0 m.

Accepted Answer

The velocity of flow of gasoline can be calculated using the Bernoulli's equation which is given as:

P₁ + (1/2)ρv₁² + ρgh₁ = P₂ + (1/2)ρv₂² + ρgh₂

where:
P₁ = pressure at the higher level
v₁ = velocity of flow at the higher level (unknown)
h₁ = height at the higher level (1.0 m)
P₂ = pressure at the lower level
v₂ = velocity of flow at the lower level (unknown)
h₂ = height at the lower level (0 m, since the outlet is at the same level as the lower surface of the liquid)
ρ = density of gasoline

Assuming that the pressure at both levels is atmospheric pressure and that the flow is steady (i.e., v₁ = v₂), the equation simplifies to:

(1/2)ρv₁² + ρgh₁ = 0 + (1/2)ρv₂² + ρgh₂

Solving for v₁, we get:

v₁ = sqrt((2gh) + v₂²)

Since the fluid is incompressible and the area of the tube is constant, the volume flow rate Q is given by:

Q = Av = constant

where A is the cross-sectional area of the tube. Therefore, the velocity of flow at the lower level is:

v₂ = Q/A

Substituting the given values, we get:

v₂ = (6000/π)/[(3/1000)²π/4] = 8 m/s

Substituting this value and h₁ = 1.0 m into the equation for v₁, we get:

v₁ = sqrt((2 x 9.81 x 1.0) + 8²) = 4.4 m/s

Therefore, the velocity of flow of gasoline is 4.4 m/s. The best choice is C).

Question 12

A thin rectangular piece of wood floats in water. You slowly pour oil with a density equal to that of the wood on the surface of the water until the height of the oil above the water is twice the height of the piece of wood. Which statement is correct?

Accepted Answer

Since the density of the oil is equal to that of the wood, the wood will float at the interface between the oil and water, not changing its buoyancy significantly but adjusting its position so that it floats in the oil just above the water. This is because objects float at a level where the fluid (or fluids, in this case) can provide enough buoyant force to counteract the object's weight, and since the oil and wood have the same density, the wood will float in the oil layer.

Question 13

In a wind tunnel the pressure on the top surface of a model airplane wing is 8.8 × 10⁴ N/m and the pressure on the bottom surface is 9.0 × 10⁴ N/m². If the area of the top and bottom surfaces of each wing is 2.0 m², what is the total lift on the model airplane?

Accepted Answer

The answer of In a wind tunnel the pressure on...

Question 14

The water level in identical bowls, A and B, is exactly the same. A contains only water; B contains floating ice as well as water. When we weigh the bowls, we find that

Accepted Answer

The answer of The water level in identical bowls, A...

Question 15

Air within the funnel of a large tornado may have a pressure of only 0.2 ATM. What is the approximate outward force on a (5 m × 10 m) wall if a tornado suddenly envelops the house? (1 ATM = 1.01 × 10⁵ N/m².)

Accepted Answer

The answer of Air within the funnel of a large...

Question 16

A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 meters. What is the maximum power output if 30.0% of the wind's energy can be extracted? ρ_air = 1.25 kg/m³.

Accepted Answer

The power output of a wind turbine is given by the formula P = 0.5 ρ A v^3, where ρ is the density of air, A is the area swept out by the blades, and v is the velocity of the wind. Here, we are given ρ = 1.25 kg/m^3, A = πr^2 = 25π m^2, v = 10 m/s, and a efficiency of 30% or 0.3. Therefore, the power output is:

P = 0.5 ρ A v^3 × 0.3 = 0.5 × 1.25 × 25π × 10^3 × 10^3 × 10^3 × 0.3 = 14.7 kW.

The best choice is B, 14.7 kW, because it correctly uses the formula for power output of a wind turbine and takes into account the given values of ρ, A, v, and efficiency.

Question 17

An empty spice bottle has an inner volume of 1.31 × 10−⁴ m³. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10−⁴ m³ of water when fully submerged. What volume of mercury (ρ_Hg = 13.6 × 10³ kg/m³) must be added to the empty bottle so that it will just submerge?

Accepted Answer

To find the volume of mercury needed, we first determine the volume of the bottle using the displacement method, which is 1.63 × 10^(-4) m^3. Since the bottle needs to just submerge, the weight of the mercury added must equal the buoyant force exerted by the displaced water. The density of mercury is given as 13.6 × 10^3 kg/m^3. Using the formula for buoyant force (weight of displaced fluid), we can calculate the volume of mercury needed. The calculation involves equating the mass of displaced water (volume of the bottle times the density of water, 1000 kg/m^3) to the mass of the mercury added (volume of mercury times the density of mercury, 13.6 × 10^3 kg/m^3). Solving for the volume of mercury gives a result close to 3.75 × 10^(-5) m^3, or 3.75 cm^3 when converted to cm^3 (since 1 m^3 = 10^6 cm^3).

Question 18

People can snorkel down to a depth of roughly one meter. This means that the additional pressure on the air in their lungs is roughly

Accepted Answer

Pressure is measured in Pascal (Pa) and at a depth of one meter, the pressure exerted on the air in the lungs is approximately 9 800 Pa. Choice A is incorrect because it refers to the force of gravity on a 1 kg object and not pressure. Choice C is incorrect because it refers to the number of atmospheres of pressure, which is not equivalent to the pressure in Pascals. Choice D is incorrect because it is double the actual pressure at a depth of one meter. Choice E does not make sense as it includes units that are not applicable to pressure.

Question 19

A Boeing 737 airliner has a mass of 20 000 kg and the total area of both wings (top or bottom) is 100 m². What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude?

Accepted Answer

To keep the airplane at a constant altitude, the lift force must equal the weight of the airplane. The weight of the airplane is the mass (20,000 kg) times the acceleration due to gravity (approximately 9.8 m/s^2), which equals 196,000 N. The pressure difference required to produce this lift force can be found by dividing the lift force by the wing area (100 m^2), resulting in a pressure difference of 1,960 N/m^2.

Question 20

A cube of water ice (ρ = 0.917 × 10³ kg/m³) is placed in mercury (ρ = 13.6 × 10³ kg/m³), which is liquid at 0° Celsius. If we ignore any possible melting of the ice cube and problems with the surface tension of mercury, the fraction of the ice cube that floats above the surface of the mercury is

Accepted Answer

The fraction of the ice cube that floats above the surface of the mercury can be calculated using the principle of buoyancy, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The fraction of the volume of the ice cube that is submerged is equal to the ratio of the density of ice (0.917 × 10^3 kg/m^3) to the density of mercury (13.6 × 10^3 kg/m^3). Thus, the fraction submerged is 0.917/13.6 = 0.0674, and the fraction that floats above is 1 - 0.0674 = 0.9326, which rounds to 0.933.

Quiz 14: Fluid Mechanics