Question

An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.8 cm is 2.4 m/s. Calculate the flow speed at a location where the diameter has narrowed to 5.80 cm

Answer 1

The value is
`v_2 = 5.53 \ m /s`

Step-by-step explanation:

From the question we are told

The pipe diameter at location 1 is
`d = 8.8 \ cm = (8.8 )/(10) = 0.88 \ m`

The velocity at location 1 is
`v_1 = 2.4 \ m /s`

The diameter at location 2 is
`d_2 = 5.80 \ cm = 0.58 \ m`

Generally the area at location 1 is

`A_1 = \pi * (d^2)/( 2)`

=>
`A_1 = \pi * (0.88^2)/( 2)`

=>
`A_1 = 3.142 * (0.88^2)/( 2)`

=>
`A_1 = 1.2166 \ m^2`

Generally the area at location 1 is

`A_2 = \pi * (d_1^2)/( 2)`

=>
`A_2 = \pi * (0.58^2)/( 2)`

=>
`A_2 = 0.528 \ m^2`

Generally from continuity equation we have that

`A_1 * v_1 = A_2 * v_2`

=>
`1.2166 * 2.4 = 0.528 * v_2`

=>
`1.2166 * 2.4 = 0.528 * v_2`

=>
`v_2 = 5.53 \ m /s`