Question

A garden hose has a radius of 0.0120 m, and water initially comes out at a speed of 2.88m/s. Dasha puts her thumb over the end , which cuts its area to 1.05×10^-4 m^2.what is the new velocity of the water coming out ?

Answer 1

v = 12.4 [m/s]

Step-by-step explanation:

With the speed and Area information, we can determine the volumetric flow.

`V=v*A\\A=\pi *r^(2)`

where:

r = radius = 0.0120 [m]

v = 2.88 [m/s]

`A=\pi *(0.0120)^(2) \\A=4.523*10^(-4) [m]\\`

Therefore the flow is:

`V=2.88*4.523*10^(-4) \\V=1.302*10^(-3) [m^(3)/s ]`

Despite the fact that you cover the inlet with the finger, the volumetric flow rate is the same.

`v=V/A\\v=1.302*10^(-3) /1.05*10^(-4) \\v=12.4[m/s]`