Question

(a) What is the pressure drop due to the Bernoulli effect as water goes into a 3.00cm diameter nozzle from a 9.00cm diameter fire hose while carrying a flow of 40.0Ls? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)

Answer 1

Answer:

1.58 MPa

163 m

Explanation:

Given:

- Diameter @ inlet of nozzle D_i = 0.09 m

- Diameter @ exit of nozzle  D_f = 0.03 m

- Flow rate of water through nozzle Q = 40 L /s

- Density of water p = 997 kg/m^3

Find:

a) Pressure drop in the nozzle (P_i - P_f)

  - Compute Velocities at the two points V_i and V_f:

           Q = A*V

           40 / 1000 = pi*D_i^2 / 4 * V_i

            V_i = (4*40) / (1000*pi*(0.09)^2)

            V_i = 6.2876 m /s

            V_f = (4*40) / (1000*pi*(0.03)^2)

            V_i = 56.588 m /s

  - Apply the Bernoulli's Equation:

             (P_i - P_f) = 0.5*p* (V_f^2 - V_i^2)

              dP = 0.5*997*(56.588^2 - 6.2876^2)

             dP = 1.58 MPa

b) The maximum height the water can rise:

    Assuming the water exits the nozzle as a free stream dP = 0

        - Apply the Bernoulli's Equation:

                p*g*h = 0.5*p* (V_f^2)

                h = V^2_f / 2*g

                h = (56.588)^2 / 2*9.81

                h = 163 m