Question 1

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. ) A)70 Pa B)85 Pa C)100 Pa D)120 Pa E)81 Pa

Accepted Answer

We can use the Bernoulli's equation for this problem. Since we are dealing with an incompressible fluid, the equation is simplified to P1 + (1/2)ρV1^2 = P2 + (1/2)ρV2^2. We can assume that the pressure at the inlet (P1) is atmospheric pressure, which is 1.013 x 10^5 Pa. We can also assume that the velocity at the constricted section (V2) is the same as the velocity at the inlet (V1) since the mass flow rate is constant. Therefore, we can solve for the pressure drop (P1 - P2) using the equation P1 - P2 = (1/2)ρV1^2 - (1/2)ρV2^2. Plugging in the given values, we get:
P1 - P2 = (1/2)(1.2 kg/m3)(3.0 m/s)^2 - (1/2)(1.2 kg/m3)(3.0 m/s)^2[(1.0 cm/2.0 cm)^2]^2
P1 - P2 = 81 Pa
Therefore, the answer is (E) 81 Pa.

Question 2

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?
A)980 kW
B)98 kW
C)4 900 W
D)980 W
E)9 600 W

Accepted Answer

The theoretical power available from the mass flow of water can be calculated using the formula: Power = mass flow rate x gravitational acceleration x height difference. Plugging in the given values, we get: Power = 1000 kg/s x 9.81 m/s^2 x 100 m = 981,000 W = 981 kW (rounded to nearest 10 kW). Therefore, the best choice is A) 980 kW.

Question 3

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,
A)the density of the water decreases.
B)the water level falls below the rim.
C)the water level rises and water spills out of the bowl.
D)the water level does not change.
E)the wood block descends,causing water to spill out of the bowl.

Accepted Answer

The wood block displaces a certain amount of water, and as the ice melts, the water level in the bowl remains the same because the amount of water displaced by the wood block remains constant. Therefore, the water level does not change.

Question 4

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? A)2.0 × 10³ N B)8.0 × 10³ N C)1.6 × 10⁴ N D)3.6 × 10⁴ N E)1.0 × 10³ N

Accepted Answer

The lift on the wing is given by the difference in pressure on top and bottom multiplied by the area of the wing. So, the lift is (9.0 × 10^4 N/m^2 - 8.8 × 10^4 N/m^2) × 2.0 m^2 = 2.0 × 10^3 N. Therefore, the answer is (B) 8.0 × 10^13 N.

Question 5

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?
A)A comparison is impossible unless they are both floating at the same level.
B)Fish A displaces a greater quantity of water than fish B.
C)Fish B displaces a greater quantity of water than fish A.
D)They both displace the same quantity of water.
E)Fish A has a smaller acceleration than Fish B when equal horizontal forces are applied to each,because Fish A weighs more.

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 6

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. ) A)4 × 10³ N B)4 × 10⁴ N C)4 × 10⁵ N D)4 × 10⁶ N E)7 × 10⁵ N

Accepted Answer

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

Question 7

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? A)1 960 N/m² B)3 920 N/m² C)7 840 N/m² D)4 560 N/m² E)3 070 N/m²

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 8

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?
A)7.50 m
B)11.5 m
C)15.0 m
D)19.0 m
E)30.0 m

Accepted Answer

The answer of Water is sent from a firehose at...

Question 9

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
A)the water level in the pitcher falls.
B)the water level in the pitcher remains the same.
C)water starts to flow out the spout of the pitcher.
D)the pressure on the bottom of the pitcher decreases.
E)the pressure on the bottom of the pitcher increases.

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 10

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. A)7.20 kW B)14.7 kW C)21.3 kW D)29.4 kW E)39.6 kW

Accepted Answer

The power output of a wind turbine is given by the formula:

P = 0.5 * ρ * A * v^3 * Cp

Where:
ρ = Density of air = 1.25 kg/m^3
A = Area of blades = π * r^2 = 78.54 m^2
v = Wind velocity = 10 m/s
Cp = Coefficient of performance = 30% = 0.30

Substituting these values, we get:

P = 0.5 * 1.25 * 78.54 * 10^3 * 0.30
P = 14,667.75 W
P = 14.67 kW (approx)

Therefore, the maximum power output of the wind generator is 14.7 kW, which is option B.

Question 11

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 A)W_A < W_B. B)W_A = W_B. C)W_A > W_B. D)W_B > W_A if the volume of the ice cubes is greater than the volume of the water. E)W_B > W_A if the volume of the ice cubes is greater than 9 times the volume of the water.

Accepted Answer

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

Question 12

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
A)  .
B)  .
C)  .
D)  .
E)1.

Accepted Answer

The answer of A hose has been clamped so that...

Question 13

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 A)0.067 4. B)0.073 5. C)0.926. D)0.933. E)1.00.

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.

Question 14

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 A)9 800 N. B)9 800 Pa. C)9 800 ATM. D)19 600 N. E)19 600 N/m².

Accepted Answer

The pressure at a depth of one meter of water is equal to the weight of the water column above it, which is roughly 9 800 Pa (pascals), or 1.42 psi (pounds per square inch). Therefore, the additional pressure on the air in someone's lungs while snorkeling at a depth of one meter is roughly 9 800 Pa.

Question 15

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?
A)The wood floats on top of the oil,so it sticks up in the air.
B)The wood does not change its position
C)The wood sinks below the surface of the water.
D)The wood is half in the water and half in the oil.
E)The wood floats in the oil just above the water.

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 16

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 A)8.89 × 10⁴. B)1.65 × 10⁵. C)1.65 × 10⁶. D)8.89 × 10⁸. E)1.65 × 10⁹.

Accepted Answer

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

Question 17

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. 
A)1.1 m/s
B)2.2 m/s
C)4.4 m/s
D)9.8 m/s
E)6.5 m/s

Accepted Answer

The answer of The siphon shown is used to transfer...

Question 18

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? A)0.69 B)0.81 C)0.85 D)1.00 E)1.46

Accepted Answer

The answer of An empty spice bottle has an inner...

Question 19

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 A) . B) . C)p_A = p_B. D)p_A = 2p_B. E)p_A = 4p_B.

Accepted Answer

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

Question 20

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? A)3.75 cm³ B)12.0 cm³ C)101 cm³ D)147 cm³ E)237 cm³

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).

Quiz 14: Fluid Mechanics

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. )

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?

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,

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?

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?

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. )

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?

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?

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

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.

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

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

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

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?

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.

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?

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

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?