5. The pipe expands from an internal diameter of 3 cm toan internal diameter of
ID: 1742675 • Letter: 5
Question
5. The pipe expands from an internal diameter of 3 cm toan internal diameter of 8 cm. Water (r = 1000 kg /m3) enters from the left with velocity V1 = 7m/s and pressure p1 = 250 kPa. Assume (1) thatwater is inviscid and incompressible, and (2) that the flow isnon-turbulent.
a. What is the flow rate F (in m3/s) throughthe pipe? Is it the same at both ends? Why?
b. What is the velocity V2 at the exit (rightend)?
c. What is the static pressure p2 in the largesection (right side)? (Hint: The static pressure isin kPa, or kiloPascals. Your dynamic pressure outcome will bein Pascals.
Explanation / Answer
Giventhat the diameter is d1 = 3 cm = 0.03m and d2 =8cm = 0.08 m Initialvelocity is V1 = 7 m/s Pressure isP1 = 250 kPa = 250*103Pa ---------------------------------------------------------------------------------- (a)since the fluid is incompressible and non viscuss then the velocityis same in both endsThe rate of flow is A1*V1 = (d12 / 4 ) *V1 =------------ m3/s (b) From theequation of continuity A1*V1 = A2*V2 V2 = A1*V1 / A2 =( d12 / 4 ) *V1 / (d22 / 4 ) = ( d12 / d22) *V1 = --------- m/s (c) From theBernoulli's equation P1 + (1/2)*V12 + gh1 = P2 +(1/2)*V22 + gh2 since tube placed at the same height that is height same bothends P1 + (1/2)*V12 = P2 +(1/2)*V22 P2= P1 + (1/2)*V12 - (1/2)*V22 = ------------ Pa where = 1000 kg/m3 is the density of the fluid = ------------ Pa where = 1000 kg/m3 is the density of the fluid
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