Solve for Pump Horsepower in 1-Inch Tube with No Heat Transfer

[MonkeyMouse]

Homework Statement

This was a thermodynamics question;
A fluid is being moved by a pump though a 1inch diameter tube. The density is 100 lb/ft³ with a flow of 12 lb/s. The pressure rises 40lb_f/in. Assume there is no heat transfer. Find hp of the pump to the nearest 1/4hp.

Homework Equations

I assumed that the first law of thermodynamics was needed:
0=Q_cv-w_cv+m[(h1-h2)+(V₁²-V₂²)+g(z₁-z₂)]

The Attempt at a Solution

I assumed Q=0 but was rather confused on how to even start this equation. I believe you would need to use density relations to find the specific volume and enthalpy in order to apply the 1st law of thermodynamics? Would this be better suited to be solved in terms of fluid dynamics?

 

[Malverin]

Homework Statement

This was a thermodynamics question;
A fluid is being moved by a pump though a 1inch diameter tube. The density is 100 lb/ft³ with a flow of 12 lb/s. The pressure rises 40lb_f/in. Assume there is no heat transfer. Find hp of the pump to the nearest 1/4hp.

Homework Equations

I assumed that the first law of thermodynamics was needed:
0=Q_cv-w_cv+m[(h1-h2)+(V₁²-V₂²)+g(z₁-z₂)]

The Attempt at a Solution

I assumed Q=0 but was rather confused on how to even start this equation. I believe you would need to use density relations to find the specific volume and enthalpy in order to apply the 1st law of thermodynamics? Would this be better suited to be solved in terms of fluid dynamics?

It is said that, flow is 12 lb/s
So you can calculate the speed after the pump (you have diameter of the tube too)There is nothing about the speed before the pump, so we can assume it is zero.
Nothing is said about any diference in height of input/output too.
So

(z1-z2)=0

and because

and

you can easy calculate the power
η has to be 1, because it is said, there is no heat transfer

http://en.wikipedia.org/wiki/Pump

 

[MonkeyMouse]

Still pretty stuck, I am unsure how to get the change in P into psf from the units had once I incorporate the velocity?

 

[Chestermiller]

What is the volumetric flow rate? Neglect the temperature rise. The rate of doing shaft work is equal to the rate of change of enthalpy for the mass going through the pump. Since there is no temperature change, it is just ΔP times the volumetric flow rate.

 

[MonkeyMouse]

So just (5760lb/ft^2)(.12ft^2/s)... how would I get hp from those units?

 

[Chestermiller]

So just (5760lb/ft^2)(.12ft^2/s)... how would I get hp from those units?

1HP is 550 ft-lbs/sec.