A liquid is under stream lined motion through a horizontal pipe of non uniform cross section of the volume rate of flow at cross section a is v the volume rate of flow at cross section a/2 is
Ans:V
Non-compressible liquid? If so, then the equation of continuity applies.
The volume flow rate is constant . The velocity varies inversely as area.
so, if volume rate is constant, the answer must be V
To find the volume rate of flow at cross section a/2, we can apply the principle of continuity in fluid mechanics. According to this principle, the volume rate of flow remains constant along a streamline.
In a horizontal pipe, the volume rate of flow can be calculated using the formula:
Q = A * v
Where:
Q is the volume rate of flow
A is the cross-sectional area of the pipe
v is the velocity of the liquid
In this problem, the volume rate of flow at cross section a is given as v. Let's assume A1 is the cross-sectional area at a and A2 is the cross-sectional area at a/2.
Since the liquid is undergoing streamline motion, the volume rate of flow remains constant along the pipe. Therefore,
Q1 = Q2
A1 * v = A2 * v
Dividing both sides of the equation by v:
A1 = A2
So, the cross-sectional area at cross section a is equal to the cross-sectional area at cross section a/2. Therefore, the volume rate of flow at cross section a/2 is also v. Hence, the answer is V.