Consider a curved pipe and nozzle design as sketched in gure 1. Suppose water is
ID: 1842128 • Letter: C
Question
Consider a curved pipe and nozzle design as sketched in gure 1. Suppose water is supplied at a velocity V1, with gauge pressure p1, from the left-hand-side opening, which has area A1. After the 180 bend, the pipe cross sectional area reduces to A2. Assume that head losses are negligible, such that Bernoulli's equation may be used.
(i) Obtain an expression for the horizontal force required to hold the pipe in place;
(ii) Evaluate the force if V1 = 0:1 m/s, A1 = 6 cm2, A2 = 2 cm2;
(iii) What is the vertical force component?
Please box all answers and write legibly.
(e) Consider a curved pipe and nozzle design as sketched in figure 1. Suppose water is supplied at a velocity Vi, with gauge pressure p1, from the left-hand-side opening, which has area A1. After the 180o bend, the pipe cross sectional area reduces to A2. Assume that head losses are negligible, such that Bernoulli's equation may be used. (i) obtain an expression for the horizontal force required to hold the pipe in place; (ii) Evaluate the force if Vi 0.1 m/s, A1 6cm2, A2 2cm2; (iii) hat is the vertical force component? Figure 1: Nozzle geometry for problem le.Explanation / Answer
Assuming Steady, incompressible flow and negligible height difference.
Taking control volume as a rectangle enclosing the whole pipe.
Mass in = mass out -------- conservation of mass - continuity
Density*V1A1 = Density*V2A2
V1A1 = V2A2
0.1*6 = V2*2
V2 = 0.3 m/s in -x direction
Now applying momentum equation
Fx + density*V1A1*V1 - density*V2A2*V2 = 0
1) Fx + density*(A1V12 - A2V22 ) = 0
2) Fx = 1000*(0.0002*0.32 - 0.0006*0.12)
Fx = 0.012 N ---------------- Horintal Force
3) Since no change in velocity in y direction, No momentum change in y and hence Vertical component of force is 0.
Fy = 0.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.