Consider the pipe reducer shown as (A--B). The jointsat A and B are flexible so

Question

Consider the pipe reducer shown as (A--B). The jointsat A and B are flexible so the pipes do not transmit a force(but the fluid inside the pipes does). The pipe contains a steady state steady flowof water with a mass flowrate of 4.00 kg/s. Friction isnot negligible. Given gauge pressures: pA = 300 kPa, pB = 180 kPa.Determine the support force of the pipe acting on the mounting bracket. Clearly show the force directionacting on the bracket. Also find the % of the support force due to fluid momentum change.

Explanation / Answer

let velocity at A = V1 and velocity at B = V2

then by continuity equation :

A1.V1 = A2.V2

Db =Da/3 = 0.0et :2 m

so, pi/ 4 x Da^2 x V1 =pi/4 x Db x V2^2

so, 0.06^2 x V1 = ( 0.02)^2 xV2

so, V2 = 9 V1

now applying brnouli between point A and B

we get ;

P1/d + V1^2/2 = P2 + V2^2/2

here d= density = 1000 kg/m^3

so, 300 x 1000/1000 + V1^2/2 = 180 x 1000/1000 + (9V1)^2/2

so, V1 = 1.73 m/s

and V2 = 9 x 1.73 = 15.59 m/s

Now apllying moment conservation :

let F = force nedeed

then :

F = (P1A1 - P2A2) + m x (V1 - V2)

= ( 300x pi/4 x 0.06^2 - 180 x pi/4 x 0.02^2) + 4 x (1.73 - 15.59)/1000.

= 0.7913 - 0.05544

= 0.73586 KN = 735.86 N

% of force due to momentum = m x (V1 - V2)/0.73586

= 0.05544/0.73586

= 0.0753

7.53 %

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