Equation of Continuity: Tutorial Problems
Problem 1: The diameters of a tapering pipe at sections 1-1 and 2-2 are 100 mm and 150 mm respectively. If the velocity
of water flowing through the pipe at section 1-1 is 5 m/s. find:
(i) Discharge through the pipe, and
(ii) The velocity of water at section 2-2
[Ans. (i)0.039m3/s, (ii)2.22m/s]
Solution: let v1 and v2 be the velocities at 1-1 and 2-2 and d1 and d2 be diameters at 1-1 and 2-2.
(i)
Discharge through the pipe:
Let Q denote the discharge through the pipe.
The given pipe has only one inlet and only one outlet, therefore according to the equation of continuity, mass flow
rate through 1-1 and 2-2 is same.
ṁ = ṁ
ρ A v =ρ A v
−−−− −𝐸𝑞𝑛(1)
Assume the flow in is incompressible.
Therefore ρ = ρ and Eqn (1)becomes:
A v =A v
−−−− −𝐸𝑞𝑛(2)
But Q= A v = A v is the discharge through the pipe.
Lets use Q= A v = d ∗ v = 0.1 ∗ 5 = 0.039
Therefore discharge through the pipe is 0.039 m3/s
(ii) The velocity of water at section 2-2
From Eqn(2), A v = A v
Or
𝑣 =
=
=
∗𝑣 =
.
.
∗ 5 = 2.22
Therefore velocity at section 2-2 is 2.22 m/s
If you have any doubts or didn’t understand please watch
the video lecture. I have solved and explained it very well in
below video
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