Question 1

A pump is used to circulate SAE 10W oil at 30$\degree$C in an engine. What is the minimum pressure the pump must provide if it is to achieve a flow rate of 1L/s along a tube that is 1 m long with an inner diameter of 2 cm?
A) 1/8 atm
B) 1/4 atm
C) 1/2 atm
D) 3/4 atm
E) 1 atm

Accepted Answer

To calculate the minimum pressure required, we need to use the Poiseuille's equation:
Flow rate (Q) = (π * r^4 * ΔP) / (8 * ν * L)
Where, 
r = radius of the tube
ΔP = pressure required
ν = viscosity of the oil
L = length of the tube

Given,
Q = 1 L/s = 10^-3 m^3/s
r = 2 cm = 0.02 m
ν = viscosity of SAE 10W oil at 30°C = 0.0151 Pa.s
L = 1 m

Substituting these values in the equation, we get:
1 = (π * (0.02)^4 * ΔP) / (8 * 0.0151 * 1)
ΔP = 0.53 Pa

Now, we need to convert Pa to atm:
1 atm = 101325 Pa
Therefore,
0.53 Pa = 0.53 / 101325 atm = 5.23 x 10^-6 atm

Rounding off to the nearest 1/2 atm, we get:
Minimum pressure required = 1/2 atm

Question 2

A horizontal pipe of 50.0 cm² cross-sectional area carries a fluid of unknown density at a speed of 3.00 m/s. This pipe feeds a smaller pipe of cross section 25.0 cm². If the pressure difference between the two sections of pipe is 9.00 kPa, find the density of the fluid. A) 500 kg/m³ B) 360 kg/m³ C) 6000 kg/m³ D) 720 kg/m³ E) 670 kg/m³

Accepted Answer

The answer of A horizontal pipe of 50.0 cm² cross-sectional...

Question 3

A hurricane-strength wind is blowing at a speed of 100 km/hr over a flat square roof of 10 m per side. Assuming the inside of the house to be at 1 atm pressure and the density of air is 1.3 kg/m³, calculate the lifting force on the roof. A) 5.0 * 10³ N B) 3.8 * 10⁴ N C) 5.0 * 10⁴ N D) 1.0 * 10⁵ N E) 6.5 * 10⁴ N

Accepted Answer

The wind exerts a pressure on the roof given by the formula:
pressure = 0.5 * air density * wind speed^2
Substituting the given values,
pressure = 0.5 * 1.3 kg/m^3 * (100 km/hr)^2
           = 0.5 * 1.3 kg/m^3 * (27.8 m/s)^2
           = 1985.46 N/m^2
The roof has an area of (10 m)^2 = 100 m^2
So, the lifting force on the roof is given by:
lifting force = pressure * area
                   = 1985.46 N/m^2 * 100 m^2
                   = 198546 N
                   = 5.0 x 10^4 N
Therefore, the correct answer is option C.

Question 4

A pump is used to circulate oil in an engine. If the diameter of the tube connecting the pump to the engine is increased by a factor of 2, the ration of the resulting pressure to the initial pressure in the pipe is
A) 1/32.
B) 1/16.
C) 1/8.
D) 1/2.
E) 1/4.

Accepted Answer

The pressure in a pipe is inversely proportional to the fourth power of the diameter (according to the Hagen-Poiseuille equation for laminar flow). If the diameter is increased by a factor of 2, the pressure decreases by a factor of 2^4 = 16. Thus, the ratio of the resulting pressure to the initial pressure is 1/16.

Question 5

For the streamlined flow of a viscous liquid, such as water, in a capillary tube, which of the following is correct?
A) The coefficient of viscosity depends on the radius of the inside of the tube raised to the fourth power.
B) The velocity of the liquid is essentially zero at the tube walls and increases toward the center of the tube.
C) There is no pressure difference along the tube provided the tube is less than 10 cm in length.
D) The volume flow rate through the tube can never be constant.
E) None of these is correct.

Accepted Answer

The velocity of the liquid is essentially zero at the tube walls due to the no-slip condition, and increases toward the center of the tube, reaching a maximum at the centerline. The coefficient of viscosity, represented by the symbol η, depends on the radius of the inside of the tube raised to the power of -3, not -4 (answer A is incorrect). Pressure difference along the tube is present as long as there is a change in radius or height, regardless of the length of the tube (answer C is incorrect). It is possible to have a constant volume flow rate through the tube as long as the pressure difference across the tube remains constant (answer D is incorrect). Therefore, the correct answer is B.

Question 6

A hurricane-strength wind is blowing past a wooden box-shaped shack with its door and windows shut. Which one of the following statements is true?
A) Only the roof will feel a net force outward.
B) The shack will implode.
C) The air inside is at a lower pressure than outside.
D) The roof and some of the sides feel a net force outward.
E) The door and roof will always be pulled off together.

Accepted Answer

The air pressure difference between the inside and outside of the shack will create a net force pushing outward on the roof and some of the sides, as air will find an escape through any gaps or weaknesses. However, the door and windows being shut will prevent a complete implosion or destruction of the structure. The statement about the roof feeling a net force outward is also true, but not the only part of the shack affected.

Question 7

A hurricane-strength wind is blowing at a speed of 100 km/hr over a flat roof of 100 m². Assuming the inside of the house to be at 1 atm pressure and the density of air is 1.3 kg/m³, calculate the pressure difference between the inside and the outside of the roof. A) 500 Pa lower outside B) 1000 Pa higher outside C) 500 Pa lower inside D) 1000 Pa lower outside E) 18 Pa lower outside

Accepted Answer

The answer of A hurricane-strength wind is blowing at a...

Question 8

As part of a science project you investigate the effect of punching holes in a plastic container of water and observing the flow of liquid out of the different holes. If the container has a water level 20 cm above the base and you punch a hole in the side 12 cm high, calculate the speed at which water will initially flow out of the hole.
A) 1.25 m/s
B) 15.3 m/s
C) 12.5 m/s
D) 1.50 m/s
E) 2.25 m/s

Accepted Answer

The speed of water flowing out of the hole can be calculated using Torricelli's Law, which states that the speed $v$ of efflux of a fluid under gravity from a hole at a depth $h$ below the surface is given by $v = \sqrt{2gh}$, where $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Given that the water level is 20 cm above the base and the hole is 12 cm high, the depth $h$ of the water above the hole is $20 \, \text{cm} - 12 \, \text{cm} = 8 \, \text{cm} = 0.08 \, \text{m}$. Plugging these values into the formula gives $v = \sqrt{2 \times 9.8 \, \text{m/s}^2 \times 0.08 \, \text{m}} = \sqrt{1.568} \, \text{m/s} \approx 1.25 \, \text{m/s}$.

Question 9

Using a motion sensor, Susana finds that the acceleration of a 4-kg rock that has been dropped from the roof of a building is 6 m/s². She concludes that the magnitude of force of air resistance acting on the rock is approximately A) 39.2 N. B) 24.0 N. C) 15.2 N. D) 9.81 N. E) None of these is correct.

Accepted Answer

When an object is dropped, its acceleration is given by the equation:
a = g - (F_air/m)
where g is the acceleration due to gravity, F_air is the force of air resistance, and m is the mass of the object.

Rearranging the equation:
F_air = m(g - a)

Plugging in the given values:
F_air = 4 kg(9.81 m/s^2 - 6 m/s^2)
F_air = 15.24 N

Thus, the magnitude of the force of air resistance acting on the rock is approximately 15.2 N. Therefore, the correct choice is C.

Question 10

Using a motion sensor, Sean finds that the acceleration of a 2-kg rock that has been dropped from the roof of a building is 5.5 m/s². He concludes that the magnitude of force of air resistance acting on the rock is approximately A) 19.6 N. B) 11.0 N. C) 9.81 N. D) 6.62 N. E) None of these is correct.

Accepted Answer

The answer of Using a motion sensor, Sean finds that...

Question 11

A hypodermic needle can be thought of as a large area pipe leading to a small area pipe that opens into the vein. The diameter of the plunger is 1.2 cm and the needle diameter is 0.15 cm. If the gauge pressure in the vein is 25 mmHg, what minimum force is needed on the plunger in order for a fluid flow into the vein to occur?
A) 0.38 N
B) 0.19 N
C) 0.0060 N
D) 31 N
E) 0.12 N

Accepted Answer

To find the minimum force needed on the plunger for fluid to flow into the vein, we can use Pascal's principle, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. The force needed can be calculated using the formula $F = PA$, where $F$ is the force, $P$ is the pressure, and $A$ is the area.First, convert the gauge pressure from mmHg to Pascals (Pa) since 1 mmHg = 133.322 Pa. Thus, 25 mmHg = $25 \times 133.322 = 3333.05$ Pa.The area of the plunger ($A$) can be calculated using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the plunger. The diameter of the plunger is 1.2 cm, so the radius is $0.6$ cm or $0.006$ m (since 1 cm = 0.01 m). Therefore, the area is $A = \pi (0.006)^2 = 1.13 \times 10^{-4}$ m$^2$.The minimum force needed on the plunger is then $F = PA = 3333.05 \times 1.13 \times 10^{-4} = 0.376$ N, which rounds to $0.38$ N.

Question 12

A pipe that appears to be of uniform size has constrictions on the inside. When a liquid flows through the pipe, the pressures at various points are indicated by the heights of the columns in the manometer tubes. If fluid friction is negligible, at which point is the diameter greatest?
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The answer of  A pipe that appears to be...

Quiz 11: Fluids

A pump is used to circulate SAE 10W oil at 30 $\degree$ C in an engine. What is the minimum pressure the pump must provide if it is to achieve a flow rate of 1L/s along a tube that is 1 m long with an inner diameter of 2 cm?

A horizontal pipe of 50.0 cm² cross-sectional area carries a fluid of unknown density at a speed of 3.00 m/s. This pipe feeds a smaller pipe of cross section 25.0 cm². If the pressure difference between the two sections of pipe is 9.00 kPa, find the density of the fluid.

A hurricane-strength wind is blowing at a speed of 100 km/hr over a flat square roof of 10 m per side. Assuming the inside of the house to be at 1 atm pressure and the density of air is 1.3 kg/m³, calculate the lifting force on the roof.

A pump is used to circulate oil in an engine. If the diameter of the tube connecting the pump to the engine is increased by a factor of 2, the ration of the resulting pressure to the initial pressure in the pipe is

For the streamlined flow of a viscous liquid, such as water, in a capillary tube, which of the following is correct?

A hurricane-strength wind is blowing past a wooden box-shaped shack with its door and windows shut. Which one of the following statements is true?

A hurricane-strength wind is blowing at a speed of 100 km/hr over a flat roof of 100 m². Assuming the inside of the house to be at 1 atm pressure and the density of air is 1.3 kg/m³, calculate the pressure difference between the inside and the outside of the roof.

Using a motion sensor, Susana finds that the acceleration of a 4-kg rock that has been dropped from the roof of a building is 6 m/s². She concludes that the magnitude of force of air resistance acting on the rock is approximately

Using a motion sensor, Sean finds that the acceleration of a 2-kg rock that has been dropped from the roof of a building is 5.5 m/s². He concludes that the magnitude of force of air resistance acting on the rock is approximately

A pipe that appears to be of uniform size has constrictions on the inside. When a liquid flows through the pipe, the pressures at various points are indicated by the heights of the columns in the manometer tubes. If fluid friction is negligible, at which point is the diameter greatest?

Quiz 11: Fluids

A pump is used to circulate SAE 10W oil at 30 °\degree° C in an engine. What is the minimum pressure the pump must provide if it is to achieve a flow rate of 1L/s along a tube that is 1 m long with an inner diameter of 2 cm?

A horizontal pipe of 50.0 cm2 cross-sectional area carries a fluid of unknown density at a speed of 3.00 m/s. This pipe feeds a smaller pipe of cross section 25.0 cm2. If the pressure difference between the two sections of pipe is 9.00 kPa, find the density of the fluid.

A hurricane-strength wind is blowing at a speed of 100 km/hr over a flat square roof of 10 m per side. Assuming the inside of the house to be at 1 atm pressure and the density of air is 1.3 kg/m3, calculate the lifting force on the roof.