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Question

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5cm and 3.75 cm. The ratio of the velocities in the two pipes is according to the equation of continuity


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Solution

Step 1: Given Data

Given: Diameters of pipe through a cross-section of pipes are 2.5cm and 3.75cm.

Let A1,A2are the areas of the cross sections and v1,v2 are velocities in two pipes.

Step 2: Formula Used

According to the equation of continuity

A1v1=A2v2ā‡’v1v2=A2A1------(1)

Step 3: Calculate the Areas

Area of a circle=Ļ€d22
ā‡’A1=Ļ€d122ā‡’A1=Ļ€2.522

and A2=Ļ€d222

ā‡’A2=Ļ€3.7522

Step 4: Calculate the Ratio

From equation (1)

ā‡’v1v2=Ļ€3.7522Ļ€2.522ā‡’v1v2=3.752.52ā‡’v1v2=322ā‡’v1v2=94

Hence, the ratio of the velocities in the two pipes is 94.


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