# 14.6 Bernoulli’s equation  (Page 6/8)

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David rolled down the window on his car while driving on the freeway. An empty plastic bag on the floor promptly flew out the window. Explain why.

Based on Bernoulli’s equation, what are three forms of energy in a fluid? (Note that these forms are conservative, unlike heat transfer and other dissipative forms not included in Bernoulli’s equation.)

Potential energy due to position, kinetic energy due to velocity, and the work done by a pressure difference.

The old rubber boot shown below has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of Leak 1? Explain your responses in terms of energy.

Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.

The water has kinetic energy due to its motion. This energy can be converted into work against the difference in pressure.

## Problems

Verify that pressure has units of energy per unit volume.

$\begin{array}{}\\ \\ \hfill F& =\hfill & pA⇒p=\frac{F}{A},\hfill \\ \hfill \left[p\right]& =\hfill & {\text{N/m}}^{2}=\text{N}·{\text{m/m}}^{3}={\text{J/m}}^{3}=\text{energy/volume}\hfill \end{array}$

Suppose you have a wind speed gauge like the pitot tube shown in [link] . By what factor must wind speed increase to double the value of h in the manometer? Is this independent of the moving fluid and the fluid in the manometer?

If the pressure reading of your pitot tube is 15.0 mm Hg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude?

−135 mm Hg

Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mph) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli equation on a roof having an area of $220{\text{m}}^{2}$ ? Typical air density in Boulder is $1.14{\text{kg/m}}^{3}$ , and the corresponding atmospheric pressure is $8.89\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}{\text{N/m}}^{2}$ . (Bernoulli’s principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

What is the pressure drop due to the Bernoulli Effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)

a. $1.58\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}{\text{N/m}}^{2}$ ; b. 163 m

(a) Using Bernoulli’s equation, show that the measured fluid speed v for a pitot tube, like the one in [link] (b), is given by $v={\left(\frac{2{\rho }^{\prime }gh}{\rho }\right)}^{1\text{/}2}$ , where h is the height of the manometer fluid, ${\rho }^{\prime }$ is the density of the manometer fluid, $\rho$ is the density of the moving fluid, and g is the acceleration due to gravity. (Note that v is indeed proportional to the square root of h , as stated in the text.) (b) Calculate v for moving air if a mercury manometer’s h is 0.200 m.

A container of water has a cross-sectional area of $A=0.1\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ . A piston sits on top of the water (see the following figure). There is a spout located 0.15 m from the bottom of the tank, open to the atmosphere, and a stream of water exits the spout. The cross sectional area of the spout is ${A}_{\text{s}}=7.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}{\text{m}}^{2}$ . (a) What is the velocity of the water as it leaves the spout? (b) If the opening of the spout is located 1.5 m above the ground, how far from the spout does the water hit the floor? Ignore all friction and dissipative forces.

a. ${v}_{2}=3.28\frac{\text{m}}{\text{s}}$ ;
b. $t=0.55\phantom{\rule{0.2em}{0ex}}\text{s}$
$x=vt=1.81\phantom{\rule{0.2em}{0ex}}\text{m}$

A fluid of a constant density flows through a reduction in a pipe. Find an equation for the change in pressure, in terms of ${v}_{1},{A}_{1},{A}_{2}$ , and the density.

a particle projected from origin moving on x-y plane passes through P & Q having consituents (9,7) , (18,4) respectively.find eq. of trajectry.
definition of inertia
the reluctance of a body to start moving when it is at rest and to stop moving when it is in motion
charles
An inherent property by virtue of which the body remains in its pure state or initial state
Kushal
why current is not a vector quantity , whereas it have magnitude as well as direction.
why
daniel
the flow of current is not current
fitzgerald
bcoz it doesn't satisfy the algabric laws of vectors
Shiekh
The Electric current can be defined as the dot product of the current density and the differential cross-sectional area vector : ... So the electric current is a scalar quantity . Scalars are related to tensors by the fact that a scalar is a tensor of order or rank zero .
Kushal
what is binomial theorem
what is binary operations
Tollum
What is the formula to calculat parallel forces that acts in opposite direction?
position, velocity and acceleration of vector
hi
peter
hi
daniel
hi
Vedisha
*a plane flies with a velocity of 1000km/hr in a direction North60degree east.find it effective velocity in the easterly and northerly direction.*
imam
hello
Lydia
hello Lydia.
Sackson
What is momentum
isijola
hello
A rail way truck of mass 2400kg is hung onto a stationary trunk on a level track and collides with it at 4.7m|s. After collision the two trunk move together with a common speed of 1.2m|s. Calculate the mass of the stationary trunk
I need the solving for this question
philip
is the eye the same like the camera
I can't understand
Suraia
Josh
I think the question is that ,,, the working principal of eye and camera same or not?
Sardar
yes i think is same as the camera
what are the dimensions of surface tension
samsfavor
why is the "_" sign used for a wave to the right instead of to the left?
why classical mechanics is necessary for graduate students?
classical mechanics?
Victor
principle of superposition?
principle of superposition allows us to find the electric field on a charge by finding the x and y components
Kidus
Two Masses,m and 2m,approach each along a path at right angles to each other .After collision,they stick together and move off at 2m/s at angle 37° to the original direction of the mass m. What where the initial speeds of the two particles
MB
2m & m initial velocity 1.8m/s & 4.8m/s respectively,apply conservation of linear momentum in two perpendicular directions.
Shubhrant
A body on circular orbit makes an angular displacement given by teta(t)=2(t)+5(t)+5.if time t is in seconds calculate the angular velocity at t=2s
MB
2+5+0=7sec differentiate above equation w.r.t time, as angular velocity is rate of change of angular displacement.
Shubhrant
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
(10/6) ÷0.4=4.167 per sec
Shubhrant
what is the formula for pressure?
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus