Question

What is the pressure drop due to the Bernoulli effect as water goes into a (3.00)-cm-diameter nozzle from a (9.00)-cm-diameter fire hose while carrying a flow of (40.0 , L/s)?

a) (2.20 X 10³ , Pa)
b) (4.41 X 10³ , Pa)
c) (1.10 X 10³ , Pa)
d) (8.81 X 10³ , Pa)

Answer 1

The pressure drop due to the Bernoulli effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s is 4.41 x 10³ Pa.

Step-by-step explanation:

To find the pressure drop due to the Bernoulli effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s, we can use Bernoulli's equation.

Bernoulli's equation states that the total pressure at any point in a fluid flow system is the sum of the static pressure, the kinetic pressure, and the potential energy pressure.

Using Bernoulli's equation, we can equate the pressures at the fire hose and the nozzle, and solve for the pressure drop:

P1 + 1/2ρv12 + ρgh1 = P2 + 1/2ρv22 + ρgh2

Since the height difference is negligible, we can neglect the potential energy terms. Also, we can assume that the water is incompressible, so the density ρ is constant. This leaves us with:

P1 + 1/2ρv12 = P2 + 1/2ρv22

We can rearrange this equation to solve for the pressure drop ΔP:

ΔP = P2 - P1 = 1/2ρ(v12 - v22)

Substituting the given values, we get:

ΔP = 1/2(1000 kg/m3)(40 m/s - 13.3 m/s)2 = 4.41 x 103 Pa

Therefore, the pressure drop due to the Bernoulli effect is 4.41 x 103 Pa (option b).