Question

Water is moving at a velocity of 2.17 m/s through a hose with an internal diameter of 1.60 cm. The fluid velocity in this hose’s nozzle is 14.5 m/s. What is the nozzle’s inside diameter, in cm?

Answer 1

To find the nozzle's inside diameter, use the principle of continuity. Set up the equation A1V1 = A2V2 and solve for r2. Finally, calculate the nozzle's inside diameter.

Step-by-step explanation:

To find the nozzle's inside diameter, we can use the principle of continuity, which states that the flow rate of a fluid is constant throughout a pipe or nozzle.

The formula for continuity is A1V1 = A2V2, where A is the cross-sectional area and V is the fluid velocity.

In this case, we can set up the equation as (pi * r12) * 2.17 = (pi * r22) * 14.5, where r1 and r2 are the radii of the hose and nozzle respectively.

By rearranging the equation and solving for r2, we find that r2 = sqrt((r12 * 2.17) / 14.5).

Since the radius is half of the diameter, the nozzle's inside diameter can be calculated as 2 * r2 in cm.

Answer 2

0.619 cm

Step-by-step explanation:

V = 2.17 m/s, diameter internal, D = 1.60 cm

v = 14.5 m/s, inside diameter, d = ?

According to the equation of continuity,

A V = a v

3.14 x (1.60/2)^2 x 2.17 = 3.14 x (d/2 )^2 x 14.5

5.5552 / 4 = d^2 x 3.625

d = 0.619 cm