Engineering fluid mechanics problem

AI Thread Summary
To solve the fluid mechanics problem involving a hydroponic garden's perforated pipe system, Bernoulli's equation can be applied to analyze the flow and pressure distribution. The challenge is to design a hole-size distribution that ensures a uniform discharge flow rate along the 10 m pipe, considering the pressure variations due to the closed end. The initial pressure of 75 kPa at the entrance leads to higher flow rates near the closed end, necessitating a strategic approach to hole sizing. The solution requires selecting commercial metric drill-bit sizes to create varying hole diameters along the pipe. This design analysis aims to optimize flow uniformity while adhering to practical constraints.
luisito424
Messages
1
Reaction score
0
PLEASE, I NEED TO KNOW HOW START THIS PROBLEM.
CAN I USE BERNOULLI'S EQUATIONS?. HOW?

A hydroponic garden uses the 10 m long perforated pipe system to deliver water at 20ºC. The pipe is 5cm in diameter and contains a circular hole every 20 cm. A pump delivers water at 75 kPa (gage) at the entrance, while the other end of the pipe is closed. Pressure near the closed end of the perforated “manifold” is surprisingly high and there will be too much flow trough the holes near that end. One remedy is to vary the hole size along the pipe axis. Make a design analysis to pick the optimum hole-size distribution that will make the discharge flow rate as uniform as possible along the pipe axis. You are constrained to pick hole sizes that correspond only to commercial metric drill-bit sizes available to the typical machine shop.


Homework Equations





The Attempt at a Solution



 

Attachments

  • Engineering fluid mechanics Diagram.JPG
    Engineering fluid mechanics Diagram.JPG
    15.4 KB · Views: 1,091
Physics news on Phys.org
I have the same project for a class, did you have the solution of the excercise
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top