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Equation of Continuity is considered one of the most asked concept.
19 Questions around this concept.
Water is flowing at a speed of 1.5 ms-1 through a horizontal tube of cross-sectional area 10-2 m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force (in N) that you must exert should be (density of water=103 kgm-3).
Consider the flow is incompressible, which is shown in figure. The magnitude of velocity v is at cross section 3A, 1 m/sec is at cross section 2A, and 4 m/sec is at cross section A. Determine the value of the velocity v
The cylindrical tube of a spray pump has a radius R, one end of which has n fine holes, each of radius r. If the speed of flow of the liquid in the tube is V, the speed of ejection of the liquid through the holes is
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Water is flowing through a tube of radius r with a speed v. If this tube is joined to another tube of radius , what is the speed of water in the second tube?
A liquid flows through a pipe of varying diameter. The velocity of the liquid is at a point where the diameter is
The velocity of the liquid at a point where the diameter is
will be
Which one of the following statements is correct? When a fluid passes through the narrow part of the nonuniform pipe,
Water from a tap emerges vertically downwards with an initial speed of . The cross-sectional area of the tap is
. Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is:
A cubical box of wine has a small spout located in one of the bottom corners. When the box is full and placed on a level surface, opening the spout results in a flow of wine with a initial speed of
A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes
Two water pipes and
having diameters
and
, respectively, are joined in series with the main supply line of water. The velocity of water flowing in the pipe
is
It is applied when fluid is an ideal fluid. (means fluid is Incompressible and Non-viscous)
The equation of continuity is derived from the principle of conservation of mass.
Have a look at the flow of ideal fluid through the tube AB.
For the above figure
Let the Mass of the liquid entering per second at
The mass of the liquid leaving per second at
From Mass conservation law we can write
If the cross-sectional area of the pipe at points
Let the liquid enter with normal velocity
And
Then
But
And Since the flow is incompressible so
So Equation of Continuity for the liquid flow in tube AB is given by
The Equation of Continuity states that for the liquid flow in the tube, the product of cross-section and area remains the same at all points in the tube.
From the Equation of Continuity, we can say that
The velocity of flow will increase if the cross-section decreases and vice-versa.
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