# 14.5 Fluid dynamics  (Page 4/9)

 Page 4 / 9
${A}_{1}{v}_{1}={A}_{2}{v}_{2}.$

The equation reduces to show that the volume flow rate into the pipe equals the volume flow rate out of the pipe.

## Summary

• Flow rate Q is defined as the volume V flowing past a point in time t , or $Q=\frac{dV}{dt}$ where V is volume and t is time. The SI unit of flow rate is ${\text{m}}^{3}\text{/s,}$ but other rates can be used, such as L/min.
• Flow rate and velocity are related by $Q=Av$ where A is the cross-sectional area of the flow and v is its average velocity.
• The equation of continuity states that for an incompressible fluid, the mass flowing into a pipe must equal the mass flowing out of the pipe.

## Conceptual questions

Many figures in the text show streamlines. Explain why fluid velocity is greatest where streamlines are closest together. ( Hint: Consider the relationship between fluid velocity and the cross-sectional area through which the fluid flows.)

Consider two different pipes connected to a single pipe of a smaller diameter, with fluid flowing from the two pipes into the smaller pipe. Since the fluid is forced through a smaller cross-sectional area, it must move faster as the flow lines become closer together. Likewise, if a pipe with a large radius feeds into a pipe with a small radius, the stream lines will become closer together and the fluid will move faster.

## Problems

What is the average flow rate in ${\text{cm}}^{3}\text{/s}$ of gasoline to the engine of a car traveling at 100 km/h if it averages 10.0 km/L?

2.77 ${\text{cm}}^{3}\text{/s}$

The heart of a resting adult pumps blood at a rate of 5.00 L/min. (a) Convert this to ${\text{cm}}^{3}\text{/s}$ . (b) What is this rate in ${\text{m}}^{3}\text{/s}$ ?

The Huka Falls on the Waikato River is one of New Zealand’s most visited natural tourist attractions. On average, the river has a flow rate of about 300,000 L/s. At the gorge, the river narrows to 20-m wide and averages 20-m deep. (a) What is the average speed of the river in the gorge? (b) What is the average speed of the water in the river downstream of the falls when it widens to 60 m and its depth increases to an average of 40 m?

a. 0.75 m/s; b. 0.13 m/s

(a) Estimate the time it would take to fill a private swimming pool with a capacity of 80,000 L using a garden hose delivering 60 L/min. (b) How long would it take if you could divert a moderate size river, flowing at ${5000\phantom{\rule{0.2em}{0ex}}\text{m}}^{3}\text{/s}$ into the pool?

What is the fluid speed in a fire hose with a 9.00-cm diameter carrying 80.0 L of water per second? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if salt water replaced the fresh water in the fire hose?

a. 12.6 m/s; b. $0.0800\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}\text{/s}$ ; c. No, the flow rate and the velocity are independent of the density of the fluid.

Water is moving at a velocity of 2.00 m/s through a hose with an internal diameter of 1.60 cm. (a) What is the flow rate in liters per second? (b) The fluid velocity in this hose’s nozzle is 15.0 m/s. What is the nozzle’s inside diameter?

Prove that the speed of an incompressible fluid through a constriction, such as in a Venturi tube, increases by a factor equal to the square of the factor by which the diameter decreases. (The converse applies for flow out of a constriction into a larger-diameter region.)

If the fluid is incompressible, the flow rate through both sides will be equal:

$Q={A}_{1}{\stackrel{\text{–}}{v}}_{1}={A}_{2}{\stackrel{\text{–}}{v}}_{2},$ or $\pi \frac{{d}_{1}^{2}}{4}{\stackrel{\text{–}}{v}}_{1}=\pi \frac{{d}_{2}^{2}}{4}{\stackrel{\text{–}}{v}}_{2}⇒{\stackrel{\text{–}}{v}}_{2}={\stackrel{\text{–}}{v}}_{1}\left({d}_{1}^{2}\text{/}{d}_{2}^{2}\right)={\stackrel{\text{–}}{v}}_{1}{\left({d}_{1}\text{/}{d}_{2}\right)}^{2}$

Water emerges straight down from a faucet with a 1.80-cm diameter at a speed of 0.500 m/s. (Because of the construction of the faucet, there is no variation in speed across the stream.) (a) What is the flow rate in ${\text{cm}}^{3}\text{/s}$ ? (b) What is the diameter of the stream 0.200 m below the faucet? Neglect any effects due to surface tension.

#### Questions & Answers

what is electromagnetism
David Reply
It is the study of the electromagnetic force, one of the four fundamental forces of nature. ... It includes the electric force, which pushes all charged particles, and the magnetic force, which only pushes moving charges.
Energy
what is units?
Subhajit Reply
units as in how
praise
What is th formular for force
Joseph Reply
F = m x a
Santos
State newton's second law of motion
Seth Reply
can u tell me I cant remember
Indigo
force is equal to mass times acceleration
Santos
The acceleration of a system is directly proportional to the and in the same direction as the external force acting on the system and inversely proportional to its mass that is f=ma
David
The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
Asad Reply
Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?
Sohail Reply
how can one calculate the value of a given quantity
Helen Reply
means?
Manorama
To determine the exact value of a percent of a given quantity we need to express the given percent as fraction and multiply it by the given number.
AMIT
meaning
Winford
briefly discuss rocket in physics
Ibrahim Reply
ok let's discuss
Jay
What is physics
Nura Reply
physics is the study of natural phenomena with concern with matter and energy and relationships between them
Ibrahim
a potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inductance of the inductor that should be connected to the capacitor for the circuit to oscillate at 1125Hza potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inducta
Royalty Reply
L= 0.002H
NNAEMEKA
how did you get it?
Favour
is the magnetic field of earth changing
tibebeab Reply
what is thought to be the energy density of multiverse and is the space between universes really space
tibebeab
can you explain it
Guhan
Energy can not either created nor destroyed .therefore who created? and how did it come to existence?
Suzana Reply
this greatly depend on the kind of energy. for gravitational energy, it is result of the shattering effect violent collision of two black holes on the space-time which caused space time to be disturbed. this is according to recent study on gravitons and gravitational ripple. and many other studies
tibebeab
and not every thing have to pop into existence. and it could have always been there . and some scientists think that energy might have been the only entity in the euclidean(imaginary time T=it) which is time undergone wick rotation.
tibebeab
What is projectile?
Nana Reply
An object that is launched from a device
Grant
2 dimensional motion under constant acceleration due to gravity
Awais
Not always 2D Awais
Grant
no comments
Awais
why not? a bullet is a projectile, so is a rock I throw
Grant
bullet travel in x and y comment same as rock which is 2 dimensional
Awais
components
Awais
no all pf you are wrong. projectile is any object propelled through space by excretion of a force which cease after launch
tibebeab
for awais, there is no such thing as constant acceleration due to gravity, because gravity change from place to place and from different height
tibebeab
it is the object not the motion or its components
tibebeab
where are body center of mass on present.
Balwant Reply
on the mid point
Suzana
is the magnetic field of the earth changing?
tibebeab
does shock waves come to effect when in earth's inner atmosphere or can it have an effect on the thermosphere or ionosphere?
tibebeab
and for the question from bal want do you mean human body or just any object in space
tibebeab
A stone is dropped into a well of 19.6m deep and the impact of sound heared after 2.056 second ,find the velocity of sound in air.
Sisco Reply
9.53 m/s ?
Kyla
In this case, the velocity of sound is 350 m/s.
Zahangir
why?
Kyla
some calculations is need. then you will get exact result.
Zahangir
i mean how? isn't it just a d over t?
Kyla
calculate the time it takes the stone to hit the ground then minus the stone's time to the total time... then divide the total distance by the difference of the time
Snuggly
awit lenard. Hahahah ari ga to!
Kyla

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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