Question

1. A constriction meter in a 2-inch diameter pipeline consists of a short section of 1.2-inch diameter pipe (as shown below). The contraction and expansion are abrupt with 0 = 180 degrees. When the flow rate is 0.19 cfs the pressure at point 1 is 14 psi. (a) For this flow rate, calculate the level of the energy grade line (EGL) and hydraulic grade line (HGL) before the contraction (point 1), in the contraction (point 2) and after the expansion (point 3). Account for local losses only (neglect pipe friction losses). (b) Draw the EGL and HGL. (c) Explain why the EGL and HGL in the figure below are curved rather than straight.

Answer 1

Ans a) Pressure head = P / $\rho$g

Velocity head = V² /2g

Datum head = z

Since, all points are at equal elevation , datum head ,z = 0

we know EGL = Pressure head + Datum head & Velocity head HGL - Pressive head & Datum head Bessure at point 1, Pi= 1 upsi or 2016ps/ Diameter (D) = 2 in Diameta Cd) - 1.2.17 Flow Mate (8) - 0.19cps. tve fence, D 8= A XV. rol = = for large diameter pipe, A=C2) = 3.14in? A= 3.14 in² or 0.0218 ft²

- V = 0.19 8.716 f418. 0.0218 for small chameter pipe, A= (1-2)² = 1.13 in?.. A=1-13in² of 0.00785 ft ². - v = 0.19 - 24.2 ft 18 S-E410.0.00785 At point 1, o R 14x12x12 ft = 32.41 ft. Tg 62.2 V2 (8.716) ² = 1.18ft. 28 2x32.2 s.se z = 0 0 EGL level = 33.59 ft John HGL lvl = 32.41ft- At point 2 Apply Bernoulli enn betiveon point 1& 2,

I Loss coefficient k = 0.357 = 32.41+1-18= P2 & 9.09 +3-18. 38 = P2 = 21.32 ftch 88 ? V22 = 24. 2² 6 9.09 ft ag 2x32.2 S. Sex EGL level = 21.32 +9.09 = 30.41ff HGL level = 21.32 ft. 7 At point 3, Apply Bernoulli equation between point 123 Pit 2 P3 & V.24 EKV? 368 39 48

0.35+ 3.2 =3.55 Ex=0.35+ > 32.4+1-18 = pa + 4.18.41.18 = $z= 28.2347 12 = (8.716) 2 = 1.18 t. ag 2x32.2 o EGL level = 29.41 ft. HGL level = 28.2344 3241 ĥ I EGL - 129.41' . Vig HGL 33.54 28123 28,23 21.32'

Ans (c) The EGL and HGL are curved due to sudden change in pressure and velocity head due to expansion and contraction of pipe in which fluid is flowing .