2. * Venturi effect Now consider a tube where h1 = h2
Therefore, Bernoulli's equation remains:
P1 P2
v1
v2
P1 + ½ρv1
2 = P2 + ½ρv2
2
So…
P1 – P2 = ½ρ(v2
2 – v1
2)
If v1 > v2, then P1 – P2 < 0
And this happens only if P2 > P1
Therefore, it can be affirmed that where the speed is greater, the pressure is
less, or also, that where the speed is less, the pressure is greater.
3. Some explanations from the Venturi effect
• On a highway, if two vehicles pass
close by, in the space between them
the air moves at a high speed with
respect to the vehicles, therefore in
that area the air pressure decreases
and with this it is justified that the
vehicles attract each other . This is
more apparent if one of the vehicles is
much smaller than the other.
v1
3
P
Pinterior Airspeed
F
v2
It therefore has to...
P > Interior
therefore the smaller vehicle is attracted to the
larger one.
4. * Venturi tube
• To apply the fluid mechanics equations it is necessary to
observe the stream lines
5. • The meter shown in the figure consists of a tube with a gradual narrowing
and also a gradual increase practiced in order to avoid the formation of
eddies, thus ensuring a stationary (permanent) regime.
6.
7. According to the continuity equation
A1v1 = A2v2, entonces v2 = A1v1/A2
On the other hand, according to Bernoulli's
equation, in the Venturi effect, we have:
P1 – P2 = ½ρ(v22 – v12)
Replacing v2
P1 – P2 = ½ρ(A1
2v1
2/A2
2 – v1
2)
It is a tube where there is a narrowing. This
can be seen in the figure, where in one
sector there is a section of area A1 and in
another it has a section reduced to A2.
In the larger sector the velocity of the
fluid is v1 and in the smaller the velocity
increases to v2.
If v1 is cleared, we will have:
1
A
A
P
P
2
v
2
2
2
1
2
1
1
8. • To determine the flow, firstly, the flow rate
of the fluid is determined by applying the
continuity equation between points 1 and 2.
On the other hand, applying Bernoulli's
equation between points 1 and 2, we have
• Observing the figure, it can be
seen that z1 and z2 are at the same
horizontal level, so
Combining equations 1 and 2
9. • The pressure difference is determined
from the readings of the manometers, that
is,
Then the speed is expressed in the
form
Then the flow rate Q or volumetric
flow regime is expressed in the form
10. Example
• Suppose a pond with water has a small hole at the bottom. Based on the
information in the figure shown: with what speed does the water jet come
out of the hole?
11. * Tubo de Pitot
Este dispositivo se utiliza para medir la
velocidad del flujo de un gas, consiste en un
tubo manométrico abierto que va conectado a
una tubería que lleva un fluido como se
muestra en la Figura
La diferencia de presiones se
determina del manómetro
12. Ex1
• From a very large tank water comes out through a pipe 10 inches in
diameter, which by means of a reduction passes to 5 inches; then
discharge freely into the atmosphere. If the flow at the outlet is 105
liters/second, calculate:
a) The pressure in the initial section of the pipe
b) The height of the water in the tank measured on the axis of the pipe
c) The hydraulic power of the jet at the outlet of the pipe
13. Ex 2
• In the figure, the inside diameters of the duct in sections 1 and 2 are 50
mm and 100 mm, respectively. In section 1, water flows at 70°C with an
average speed of 8 m/s. Determine: (a) the velocity in section 2, (b) the
flow
14. Ex 3
• The figure shows a very large reservoir containing a liquid of density 0.8
subjected to a pressure of 300 kPa. The reservoir discharges to the
atmosphere through a 10-cm-diameter pipe. Determine the velocity, flow
rate, and pressure. pressure in the axis of the discharge pipe
15. Ex 4
• A large open tank contains a layer of oil floating on the water as shown in
the figure. The flow is stable and has no viscosity. Determine: (a) the
velocity of the water at the nozzle outlet (b) the height h to which the water
exiting a 0.1-m-diameter nozzle will rise.
16. Ex 5
• Water flows continuously from an open tank as shown in the figure. The
height of point 1 is 10 m, and that of points 2 and 3 is 2 m. The cross-
sectional area at point 2 is 0.03 m2, at point 3 it is 0.015 m2. The tank area
is very large compared to the cross sectional area of the tube. Determine:
(a) the volumetric flow rate and (b) the gauge pressure at point 2.
