Question

Agricultural irrigation uses a significant amount of water, and in some regions it has overwhelmed other water needs. Suppose water is drawn from a reservoir and delivered into an irrigation ditch. For most of the length of the ditch, the delivery is through a 10-cm ID pipe, and in the last few meters the pipe diameter is 7 cm. The exit from the pipe is 300 m lower than the pipe inlet.

(a) Assume that the pipe is smooth (i.e., ignore friction) and that the delivery rate is 4000 kg/h. Estimate the required pressure difference between pipe inlet and outlet. How far below the surface of the reservoir is the pipe inlet?

(b) How would your answer be different if the pipe were not smooth? Explain.

(c) What are possible environmental impacts of diverting significant quantities of river water for use in irrigation? Cite at least two sources for your response.

Answer 1

a)

Here to find the pressure difference we can use bernoulli equation as no friction losses as pipe is smooth and pressure/velocity variations are there.

so firstly we have m2= delivery mass flow rate= 4000kg/hr

m=d*a*v

where d is density, a is area, v is velocity

d=1000kg/m³; a= 3.14*d²/4 = 3.14*7²/4 = 38.465 cm²

therefore 4000=1000*38.465*v

v=10.4 m/sec

now we have P₁-P₂ = 0.5*d*(V₂²-V₁²)+d*g*(H₂-H₁) = 0.5*1000*(10.4²)+ 1000*9.8*300 = 2.994 MPa = 29.55 atm

therefore how far below the surface reservoir is the pipe inlet is given by

P-P₀ = d*g*h = (29.55-1)*10⁵*1.013 = 1000*9.8*h = 291.3 metres

b) ifthe pipe is not smooth friction is present and bernoullis equation is replaced with kinetic energy and potential energy correction factors and answer would vary.

c) increaing erosion, increasing pollution of surface water and ground water from agriculture biocides, deterioration of water quality. pollution of rivers Godavari and Krishna in india due to irrigation projects.