Question

A horizontal pipe narrows from a radius of 0.250 m to 0.1000 m. If the speed of the water in the pipe is 1.00 m/s in the larger-radius pipe, what is the speed in the smaller pipe? Given the density of water is 1000 kg/m3 , what is the mass flow rate, kg/s, of the water through the pipe?

Answer 1

6.25 m/s

196 kg/s

Step-by-step explanation:

The areas of the pipe from big to small:

`A = \pi R^2 = \pi*0.25^2 = 0.196 m^2`

`a = \pi r^2 = \pi*0.1^2=0.0314m^2`

As the product of speed and cross-section area is constant, the speed in the smaller pipe would be

`AV = av`

`v = (AV)/(a) = (0.196 * 1)/(0.0314) = 6.25 m/s`

The mass flow rate would be:

`\dot{m} = \ro AV = 1000 * 0.196 * 1 = 196 kg/s`