Help using Bernoulli's equation

In summary, the problem involves the flow of water through a hose and nozzle, and the question asks for the speed of the water and the pressure at the pump. The correct answer for the water speed is 61 m/s, and the pressure at the pump can be calculated using the equation P1 + .5p(v1)^2 = P2 + .5p(v2)^2, with P1 being the pressure at the pump, p being the density of water (1000 kg/m^3), v1 being the speed of the water at the pump (0.61 m/s), and v2 being the speed of the water at the nozzle (61 m/s). The resulting answer for P1 should be in units of
  • #1
lilmul123
40
0

Homework Statement



Water flows at 0.61 m/s through a 3.0 cm diameter hose that terminates in a 0.30 cm diameter nozzle. Assume laminar non-viscous steady-state flow.

(a) At what speed does the water pass through the nozzle? (Correctly solved to be 61 m/s).

(b) If the pump at one end of the hose and the nozzle at the other end are at the same height, and if the pressure at the nozzle is 1 atm, what is the pressure at the pump in atm?


Homework Equations



P1 + .5p(v1)^2 = P2 + .5p(v2)^2

P1 = Looking for this
p = 1000 kg/m^3 ??
v1 = .61 m/s
v2 = 61 m/s
P2 = 1 atm


The Attempt at a Solution



I plugged in all known variables, but P1 ended up being a very large number (1860314.95 atm), and this was incorrect. I'm thinking that possibly the density that I'm using is incorrect. Can anyone see what I am doing incorrectly?
 
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  • #2
Most of your quantities are in metric (MKS) units, so the pressure will have to be converted to those units first.
 
  • #3
Thanks! I wasn't sure about those units either.
 

Related to Help using Bernoulli's equation

What is Bernoulli's equation?

Bernoulli's equation is a fundamental principle in fluid dynamics that relates the pressure, velocity, and elevation of a fluid in a steady flow. It states that the sum of the dynamic pressure, static pressure, and potential energy per unit volume of a fluid is constant along a streamline.

How is Bernoulli's equation used in science?

Bernoulli's equation is used to analyze and predict the behavior of fluids in various applications, such as in pipes, pumps, and airfoils. It is also used to calculate the lift and drag forces on objects in a fluid flow, and to understand the phenomena of lift and stall in aerodynamics.

What are the assumptions of Bernoulli's equation?

Bernoulli's equation assumes that the fluid is incompressible, inviscid (no internal friction), and the flow is steady and irrotational (no vortex). It also assumes that the fluid has a constant density and the flow is along a streamline.

What are the units of Bernoulli's equation?

The units of Bernoulli's equation are typically in terms of pressure (P) and velocity (v), where the dynamic pressure is measured in units of pressure (e.g. Pa or psi) and the velocity is measured in units of speed (e.g. m/s or ft/s).

How can Bernoulli's equation be derived?

Bernoulli's equation can be derived from the principle of conservation of energy, specifically the conservation of mechanical energy. This principle states that the sum of the kinetic energy, potential energy, and internal energy of a system remains constant in the absence of external forces or energy transfers. By applying this principle to a moving fluid, Bernoulli's equation can be derived.

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