Question

the streamlines of a flow net are concentric circles.if the velocity at a radius of 0.6 m is 2.7 m/s, then the velocity at q radius of 0.9 m, will be
a)3.6 m/s
b)2.7 m/s
c)1.8 m/s
d)1.2 m/s
​

Answer 1

Given,

v₁ = 2.7 m/s

r₁ = 0.6 m

r₂ = 0.9 m

To find,

The value of v₂

Solution,

The velocity of the fluid flowing through the pipe of radius 0.9 m is 1.2 m/s. (Option D)

We can simply solve the numerical problem by the following process.

We know that;

According to the Continuity Equation;

∴ A₁ v₁ = A₂ v₂,

which states that as the area of cross-section of the pipe increases, the velocity of the fluid decreases, and as the area of cross-section of the pipe decreases, the velocity of the fluid passing through the area increases. The area of cross-section and the velocity of the fluid flowing through the area of the cross-section are inversely proportional.

Thus,

Substituting the data given in the question in the Continuity Equation;

⇒ π (0.6)² x 2.7 = π (0.9)² x v₂

⇒ v₂ = $\frac{(0.6)^2* 2.7}{(0.9)^2}$

        = 1.2

Consequently, the velocity of the fluid flowing through the pipe of radius 0.9 m is 1.2 m/s. (Option D)