Fluids Question: Calculus, Engineering, Fluid Dynamics

Question

You are filling up a ten gallon bucket from a garden hose. The time it takes you to fill up the bucket is 30 seconds. You wonder how fast the water is coming out of the nozzle, as well as how fast the water is moving through the garden hose. The water hose is has a 1 inch diameter and the nozzle has a 1 cm diameter. Conservation of mass flow for incompressible flow, particularly the fact that m₁=m₂ where m is given in the units of mass/time. Volume flow rate can be related to mass flow rate by m=pQ where q is given in units of volume/time and p is given in mass/volume. You also remember that Q=AV where A is the cross sectional area the fluid is moving through and V is the velocity of the fluid. Density of water is 1000 kg/m³.

 

Any quick help with this would be great! I am struggling with this and the assignment is due tonight. Thanks!

Answer 1

You can use the Bernoulli Equation:

 

(P₁/γ)+(v₁²/2g)+z₁ = (P₂/γ)+(v₂²/2g)+z₂

 

where:

P/γ = the pressure head

v²/2g = the velocity head

z = the elevation

 

Remember that γ=ρg and P=γh