Answer:
the diameter of the nozzle = 3 cm
Explanation:
let the diameter of nozzle be x cm.
then, area of cross-section at nozzle = [tex]\pi\frac{x^2}{4}[/tex]
nozzle with a speed of 20 m/s, and speed of the water at the faucet is 5 m/s.
area of cross section at faucet = [tex]\pi\frac{6^2}{4}[/tex]= 9π
now , area×velocity has to be constant (since area×velocity gives volume flow rate which should be same at both ends).
therefore
5×9π = 20×π×x^2/4
=>45 = 5×x^2
=>9 = x^2
=> x = 3 cm (as 3^2 =9)
therefore, the diameter of the nozzle = 3 cm
Answer:
3 cm
Explanation:
diameter of faucet, D = 6 cm
Velocity at faucet, V = 5 m/s
velocity at nozzle, v = 20 m/s
Let the diameter of the nozzle is d.
use the equation of continuity
A x V = a x v
where, A be the area of faucet, a be the area of nozzle.
π D^2 / 4 x V = πd^2 /4 x v
D^2 x V = d^2 x v
6 x 6 x 5 = d^2 x 20
d^2 = 9
d = 3 cm
Thus, the diameter of the nozzle is 3 cm .
