Help with finding mass flow rate

[Colts]

1. Homework Statement
A pump steadily delivers water through a hose terminated
by a nozzle. The exit of the nozzle has a diameter of 0.6 cm
and is located 10 m above the pump inlet pipe, which has a
diameter of 1.2 cm. The pressure is equal to 1 bar at both the
inlet and the exit, and the temperature is constant at 20° C. The
magnitude of the power input required by the pump is 1.5 kW,
and the acceleration of gravity is g = 9.81 m/s^2. Determine
the mass flow rate delivered by the pump, in kg/s.2. Homework Equations
Not sure. I think
m_dot (deltaPE) = W

I don't know if I can use the work by the pump though.
m_dot = rho*Volumetric flow rate

3. The Attempt at a Solution
Well these are the only equations I can think of and I'm not sure if these are right. Any help where to go form here would be appreciated.

 

[KataKoniK]

Hi there,

I would approach this problem by first understanding the physical principles involved. In this case, we are dealing with fluid flow and the relationship between pressure, velocity, and mass flow rate.

The Bernoulli's equation is a useful equation to use in this situation. It states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid is constant along a streamline.

In this case, we can assume that the water is incompressible, so we can neglect any changes in the kinetic energy and use the equation in its simplified form:

P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2

Where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and h is height.

We can rearrange this equation to solve for the velocity at the pump inlet (v1) and the nozzle exit (v2):

v1 = √(2(P2-P1)/ρ + 2gh1)
v2 = √(2(P2-P1)/ρ + 2gh2)

Since we are given the pressure and height at both the inlet and exit, we can plug in the values and solve for v1 and v2.

Next, we can use the continuity equation, which states that the mass flow rate (m_dot) is equal to the density (ρ) times the volumetric flow rate (Q):

m_dot = ρQ

The volumetric flow rate can be calculated by multiplying the cross-sectional area (A) of the pipe by the velocity (v):

Q = Av

We know the cross-sectional areas of both the inlet and exit pipes, as well as the velocities calculated from the Bernoulli's equation. Therefore, we can calculate the volumetric flow rate and then use it to solve for the mass flow rate.

Finally, we can use the equation for power (P) to determine the mass flow rate:

P = m_dot * g * h

Where g is the acceleration due to gravity and h is the height difference between the inlet and exit. We know the power input (1.5 kW) and the acceleration due to gravity (9.81 m/s^2), so we can solve for the mass flow rate.

I hope this helps guide you in finding the solution to this problem.