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19. Fluid Mechanics

Density

19. Fluid Mechanics

Density

Guided videos.

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Intro to Density

Intro to Density

Specific Gravity

Specific Gravity

Density Values & Conversions

Density Values & Conversions

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Density Practice Problems

Density Practice Problems

How To Calculate Density - With Examples

How To Calculate Density - With Examples

What is density?

What is density?

The Science Classroom

What is Density? - Density Explained

What is Density? - Density Explained

The Engineering Mindset

Density Practice Problems

Density Practice Problems

The Organic Chemistry Tutor

Bozeman Science

What is Density? | Gravitation | Physics | Don't Memorise

What is Density? | Gravitation | Physics | Don't Memorise

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Practice this topic

Multiple Choice

A wooden door is 1 m wide, 2.5 m tall, 6 cm thick, and weighs 400 N. What is the density of the wood in g/cm³? (use g = 10 m/s²)

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Multiple Choice

Suppose an 80 kg (176 lb) person has 5.5 L of blood (1,060 kg/m³ ) in their body. How much of this person's total mass consists of blood? What percentage of the person's total mass is blood?

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Multiple Choice

You want to verify if a 70-g crown is in fact made of pure gold (19.32 g/cm³ ), so you lower it by a string into a deep bucket of water that is filled to the top. When the crown is completely submerged, you measure that 3.62 mL of water has overflown. Is the crown made of pure gold?

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Multiple Choice

You have three objects in front of you. Object A has a volume of

4 {cm}^{3}

. object B has a volume of

7 {cm}^{3}

. and object C has a volume of

10 {cm}^{3}

. They all have the same mass. What is the correct ranking of the objects from most dense to least dense?

Multiple Choice

Suppose a cubic box contains so much air at

0 ℃

that the mass of the air inside is equal to the mass of

1 . 0 L

of water. What would be the side length of such a box?

Multiple Choice

Different materials in the body have different densities, and therefore will tend to make a person float or sink to different extents. Which bodily material is most buoyant (helps you stay afloat the most)?

Textbook Question

A brass wire is to withstand a tensile force of 350 N without breaking. What minimum diameter must the wire have?

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Textbook Question

A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0×10^5 N is applied to each of the four sides, parallel to the side. (b) Find the displacement x (in centimeters).

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Textbook Question

In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 km and the pressure is 1.16×10^8 Pa (about 1.15×10^3 atm). (a) If a cubic meter of water is taken from the surface to this depth, what is the change in its volume? (Normal atmospheric pressure is about 1.0×10^5 Pa. Assume that k for seawater is the same as the freshwater value given in Table 11.2.)

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Textbook Question

A specimen of oil having an initial volume of 600 cm3 is subjected to a pressure increase of 3.6×10^6 Pa, and the volume is found to decrease by 0.45 cm^3. What is the bulk modulus of the material and the compressibility?

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Textbook Question

A solid gold bar is pulled up from the hold of the sunken RMS Titanic. (c) The bulk modulus of lead is one-fourth that of gold. Find the ratio of the volume change of a solid lead bar to that of a gold bar of equal volume for the same pressure change.

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Textbook Question

Stress on a Mountaineer's Rope. A nylon rope used by mountaineers elongates 1.10 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young's modulus for nylon?

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Textbook Question

A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 700 N is applied to each end of the wire. What minimum diameter is required for the wire?

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Textbook Question

Two circular rods, one steel and the other copper, are joined end to end. Each rod is 0.750 m long and 1.50 cm in diameter. The combination is subjected to a tensile force with mag-nitude 4000 N. For each rod, what are (a) the strain and (b) the elongation?

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Textbook Question

A cube 5.0 cm on each side is made of a metal alloy. After you drill a cylindrical hole 2.0 cm in diameter all the way through and perpendicular to one face, you find that the cube weighs 6.30 N. (a) What is the density of this metal?

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Textbook Question

On a part-time job, you are asked to bring a cylindrical iron rod of length 85.8 cm and diameter 2.85 cm from a storage room to a machinist. Will you need a cart? (To answer, calculate the weight of the rod.)

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Textbook Question

At one point in a pipeline the water's speed is 3.00 m/s and the gauge pressure is 5.00×10^4 Pa. Find the gauge pressure at a second point in the line, 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first.

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Textbook Question

BIO. Artery Blockage. A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before the region of blockage and finds that it is 1.20×10^4 Pa, while in the region of blockage it is 1.15×10^4 Pa. Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 cm/s, and the specific gravity of this patient's blood is 1.06. What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?

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Textbook Question

Gold Brick.You win the lottery and decide to impress your friends by exhibiting a million-dollar cube of gold. At the time, gold is selling for $1282 per troy ounce, and 1.0000 troy ounce equals 31.1035 g. How tall would your million-dollar cube be?

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Textbook Question

A small circular hole 6.00 mm in diameter is cut in the side of a large water tank, 14.0 m below the water level in the tank. The top of the tank is open to the air. Find (a) the speed of efflux of the water and (b) the volume discharged per second.

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Textbook Question

A pressure difference of 6.00 * 104 Pa is required to maintain a volume flow rate of 0.800m3/s for a viscous fluid flowing through a section of cylindrical pipe that has radius 0.210 m. What pressure difference is required to maintain the same volume flow rate if the radius of the pipe is decreased to 0.0700 m?

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Textbook Question

(a) A cylindrical tank of radius 𝑅, filled to the top with a liquid, has a small hole in the side, of radius 𝓇, at distance d below the surface. Find an expression for the volume flow rate through the hole.

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Textbook Question

A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range 𝓍. The range approaches zero as y → 0 because the water squirts right onto the ground. The range also approaches zero as y → h because the horizontal velocity becomes zero. Thus there must be some height y between 0 and h for which the range is a maximum. (a) Find an algebraic expression for the flow speed v with which the water exits the hole at height y.

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Textbook Question

20°C water flows at 1.5 m/s through a 10-m-long, 1.0-mm-diameter horizontal tube and then exits into the air. What is the gauge pressure in kPa at the point where the water enters the tube?

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Textbook Question

A 5.0-m-diameter solid aluminum sphere is launched into space. By how much does its diameter increase? Give your answer in μm.

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Textbook Question

An unknown liquid flows smoothly through a 6.0-mm-diameter horizontal tube where the pressure gradient is 600 Pa/m. Then the tube diameter gradually shrinks to 3.0 mm. What is the pressure gradient in this narrower portion of the tube?

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Textbook Question

The 30-cm-long left coronary artery is 4.6 mm in diameter. Blood pressure drops by 3.0 mm of mercury over this distance. What are the (a) average blood speed and (b) volume flow rate in L/min through this artery?

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Textbook Question

Air flows through the tube shown in FIGURE P14.63. Assume that air is an ideal fluid. (b) What is the volume flow rate?

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Textbook Question

Air flows through the tube shown in FIGURE P14.62 at a rate of 1200 cm³/s . Assume that air is an ideal fluid. What is the height h of mercury in the right side of the U-tube?

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Textbook Question

A hurricane wind blows across a 6.0 m x 15.0 m flat roof at a speed of 130 km/h.(b) What is the pressure difference?

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Textbook Question

Water from a vertical pipe emerges as a 10-cm-diameter cylinder and falls straight down 7.5 m into a bucket. The water exits the pipe with a speed of 2.0 m/s. What is the diameter of the column of water as it hits the bucket?

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Textbook Question

(b) A pressure gauge reads 50 kPa as water flows at 10.0 m/s through a 16.8-cm-diameter horizontal pipe. What is the reading of a pressure gauge after the pipe has expanded to 20.0 cm in diameter?

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Textbook Question

(a) A nonviscous liquid of density p flows at speed v₀ through a horizontal pipe that expands smoothly from diameter d₀ to a larger diameter d₁ . The pressure in the narrower section is p₀. Find an expression for the pressure p₁ in the wider section.

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Textbook Question

b. 50 cm³ of gasoline are mixed with 50 cm³ of water. What is the average density of the mixture?

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Textbook Question

a. What volume of water has the same mass as 8.0 m³ of ethyl alcohol?

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Textbook Question

A 2.0 cm ✕ 2.0 cm ✕ 6.0 cm block floats in water with its long axis vertical. The length of the block above water is 2.0 cm. What is the block's mass density?

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Textbook Question

A 6.0 m ✕ 12.0 m swimming pool slopes linearly from a 1.0 m depth at one end to a 3.0 m depth at the other. What is the mass of water in the pool?

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Textbook Question

What does the top pressure gauge read in FIGURE EX14.28?

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Textbook Question

The speed of sound in air at 20°C is 344 m/s. (a) What is the wavelength of a sound wave with a frequency of 784 Hz, corresponding to the note G5 on a piano, and how many milliseconds does each vibration take? (b) What is the wavelength of a sound wave one octave higher (twice the frequency) than the note in part (a)?

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Textbook Question

Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm.

Sketch the shape of the string at the end of (a) 6.0 s.

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Textbook Question

FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.

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Textbook Question

Earthquakes are essentially sound waves—called seismic waves—traveling through the earth. Because the earth is solid, it can support both longitudinal and transverse seismic waves. The speed of longitudinal waves, called P waves, is 8000 m/s. Transverse waves, called S waves, travel at a slower 4500 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 2.0 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

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Textbook Question

Draw the history graph D(x = 4.0 m, t) at x = 4.0 m for the wave shown in FIGURE EX16.4.

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Textbook Question

A hammer taps on the end of a 4.00-m-long metal bar at room temperature. A microphone at the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through the air. The pulses are separated in time by 9.00 ms. What is the speed of sound in this metal?

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Textbook Question

A 1000 Hz sound wave traveling through 20°C air causes the pressure to oscillate around atmospheric pressure by ±0.050%. What is the maximum speed of an oscillating air molecule? Give your answer in mm/s.

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Textbook Question

A 20.0-cm-long, 10.0-cm-diameter cylinder with a piston at one end contains 1.34 kg of an unknown liquid. Using the piston to compress the length of the liquid by 1.00 mm increases the pressure by 41.0 atm. What is the speed of sound in the liquid?

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Textbook Question

Two loudspeakers in a 20°C room emit 686 Hz sound waves along the x-axis. b. If the speakers are out of phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum constructive?

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Textbook Question

Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm. a. What is the wavelength of the sound?

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Textbook Question

A hollow aluminum sphere with outer diameter 10.0 cm has a mass of 690 g. What is the sphere's inner diameter?

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