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Chapter 1: Q40E (page 392)

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

Expert verified

Velocity of water in narrow pipe = 37.5 cm/s

Step by step solution

01

Identification of given data

  • Diameter of wide pipe = 2.5 inch
  • Diameter of narrow pipe = 1inch
  • Velocity of water in wide pipe = 6cm / s
02

Significance of volume flow rate.

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

03

To calculate velocity of water in narrow pipe

Q=v×A

As volumetric flow is same in both pipes,

V1A1=V2A2A=π4d2V1π4d12=V2π4d22

Putting value in equation we get,

v2=37.5cm/s

Thus, Velocity of water in narrow pipe is

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