We were discussing the various basic concepts such
as Euler’s Equation of motion, Bernoulli’s equation from Euler’s equation,
derivation
of discharge through venturimeter and derivation of discharge through Orifice meter, in the subject of fluid mechanics, in our recent posts.Â
Let us recall the Bernoulli’s equation and applying at section 1 and section 2.
We will have following equation after applying Bernoulli’s equation at section 1 and section 2.
We had already seen the application of Bernoulli’s
equation in the working principle of Venturimeter and orifice meter. Now we
will go ahead to find out the other practical applications of Bernoulli’s
equation, in the subject of fluid mechanics, with the help of this post.
Today we will see here the basic concept of Pitot
tube and also we will secure here the expression of velocity of flow at any
point in the pipe or channel with the help of this post.
Pitot TubeÂ
Pitot tube is basically defined as a device which is
used for measuring the velocity of flow at any point in the pipe or a channel.
Working Principle of Pitot tube
Pitot tube works on the principle of Bernoulli’s
equation. If the velocity of flow at a point decreases, pressure will be
increased at that point due to the conversion of kinetic energy in to pressure
energy.
Pitot tube will be made of a glass tube bent at
right angle as displayed here in following figure. Lower end of Pitot tube
will be bent at right angle and will be directed in upstream direction as
displayed here.
Due to conversion of kinetic energy in to pressure
energy, liquid will rise up in the glass rube. Rise of liquid level will
provide the velocity of flow at any point in the pipe or a channel.
Derivation of veloctiy of flow through pitot tube
Let us consider one pitot tube as displayed here in following figure. Let us say that water is flowing through
the horizontal pipe.
P1Â = Pressure at section 1 (Inlet
section)
v1Â = Velocity of fluid at section 1
(Inlet section)
A1Â = Area of pipe at section 1
(Inlet section)
P2Â = Pressure at section 2
v2Â = Velocity of fluid at section 2
A2Â = Area at section 2
H = Depth of tube in the liquid
h = Rise of kiquid in the tube above the free
surface.
Let us recall the Bernoulli’s equation and applying at section 1 and section 2.
According to Bernoulli’s theorem.....
In an incompressible, ideal fluid when the flow is
steady and continuous, the sum of pressure energy, kinetic energy and potential
energy will be constant along a stream line.
Assumptions
Assumptions made for deriving the expression for velocity of flow at any point in the pipe or channel is as mentioned here.
1. Fluid is ideal, i.e. inviscid and incompressible.
2. Fluid flow is steady and continuous
3. Fluid flow is irrotational
4. Frictionless inner surface
We will have following equation after applying Bernoulli’s equation at section 1 and section 2.
We will now find out the momentum equation, in
the subject of fluid mechanics, in our next post.
Do you have any suggestions? Please write in comment
box.
Reference:
Fluid mechanics, By R. K. Bansal
Image Courtesy: Google
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