Question

You need to extend a 2.50-inch-diameter pipe, but you have only a 1.00-inch-diameter pipe on hand. You make a fitting to connect these pipes end to end. If the water is flowing at 6.00 cm/s in the wide pipe, how fast will it be flowing through the narrow one?

Short answer

Velocity of water in narrow pipe = 37.5 cm/s

Step-by-step solution

Identification of given data

• Diameter of wide pipe = 2.5 inch
• Diameter of narrow pipe = 1inch
• Velocity of water in wide pipe = 6cm / s

Significance of volume flow rate.

The volume flow rate is calculated as the product of flow velocity and cross-sectional vector area.

To calculate velocity of water in narrow pipe

$Q=v\times A$

As volumetric flow is same in both pipes,

$\begin{array}{r}{V}_1{A}_1=V_2{A}_2\\ A=\frac{\pi }{4}{d}^2\\ V_1\frac{\pi }{4}{d}_1^2=V_2\frac{\pi }{4}{d}_2^2\end{array}$

Putting value in equation we get,

$v_2=37.5cm/s$

Thus, Velocity of water in narrow pipe is