Question

A 10 cm diameter pipe carrying water at 1.4 m/s changes to 15 cm diameter. Calculate veocity at 15 cm diameter pipe. 0.62 m/s 0.93 m/s 2.10 m/s 1.07 m/s​

Answer 1

A 10 cm diameter pipe carrying water at 1.4 m/s changes to 15 cm diameter. Calculate veocity at 15 cm diameter pipe. 0.62 m/s 0.93 m/s 2.10 m/s 1.07 m/s

Answer 2

Given,

Pipe diameter on one end = 10 cm = 0.1 m,

Velocity on one end = 1.4 m/s,

Diameter at the other end = 15 cm = 0.15 m.

To find,

Velocity at the other end.

Solution,

The velocity of a fluid as water, in this case, flowing through a pipe of varying diameter, on any one of the ends can be determined with the help of the continuity equation, according to which,

$A_1v_1=A_2v_2$     ...(1)

Where subscripts 1, and 2 represent the two ends where fluid enters and exits the pipe respectively,

A is the cross-sectional area, and

v is the velocity.

Given that v₁ = 1.4 m/s, d₁ = 0.10 m, and d₂ = 0.15 m.

First, determining cross-sectional areas,

$A_1=\frac{\pi}{4} (d_1)^2$

⇒ $A_1=\frac{\pi}{4} (0.1)^2=0.00785m^{2}$

⇒ A₁ = 0.0079 m².

And, $A_2=\frac{\pi}{4} (d_2)^2$

⇒ $A_2=\frac{\pi}{4} (0.15)^2=0.01767m^{2}$

⇒ A₂ = 0.0177 m².

Now, using the equation (1),

$(0.0079)(1.4)=(0.0177)v_2$

Rearranging and simplifying,

$v_2=\frac{0.0079\times 1.4}{0.0177}$

⇒ $v_2=0.624858 \hspace{3} m/s$

⇒ v₂ = 0.62 m/s.

Therefore, the velocity at the 15 cm diameter of the pipe will be 0.62 m/s. (option first)