D1=30cm D2=13cm, Q(flow rate)=0.2m3/s, find loss due to sudden

[abhaiitg]

D1=30cm D2=13cm, Q(flow rate)=0.2m3/s, find loss due to sudden contraction and compare it with gradual contraction.

head loss due to suddden contraction is given by (resistance coffiecent* v*v/2*g)
and resistance cooficent is given by (1-(d2/d1)sq)sq) d2 being smaller dia of pipe..
by this we get
resistance coficent k= (1-(13/30)sq)sq=0.659
and head loss as 7.635m
now for gradual loss the resistance cofficent depends on angle it would be
for angle<45 k= 8sin θ/2(1-(d2/d1)sq)sq)
for 45>θ>180 k=(√5sinθ/2)(1-(d2/d1)sq)sq)

the answer is : (v2)^2/2g *(1/Cc-1)^2

cc= 0.63 + 0.37(A2/A1)^3

for gradual loss i don't know the formula :-| , if there is one apart from (v2^2-v1^2)/2g using bernoulli

 

[Achy47]

's equation

Hello scientist,

Thank you for your response! Let's work through the calculations together to find the loss due to sudden and gradual contraction.

First, let's calculate the velocity at the smaller diameter, v2, using the flow rate and the cross-sectional area of the pipe.

v2 = Q/A2 = (0.2m3/s)/((π/4)(0.13m)^2) = 3.14 m/s

Now, let's calculate the velocity at the larger diameter, v1, using the continuity equation.

v1 = (A2/A1)*v2 = ((π/4)(0.13m)^2)/((π/4)(0.3m)^2)*3.14 m/s = 0.24 m/s

Next, we can calculate the head loss due to sudden contraction using the formula you provided.

h = (v2)^2/2g * (1/Cc - 1)^2 = (3.14 m/s)^2/(2*9.8 m/s^2) * (1/0.659 - 1)^2 = 7.64 m

Now let's move on to gradual contraction. The formula you mentioned, (v2^2-v1^2)/2g, is correct for the head loss due to gradual contraction. However, we also need to consider the contraction coefficient, Cc, which takes into account the angle of the gradual contraction. Since we don't know the angle, we will use the average value of 0.63 for Cc.

h = (v2^2-v1^2)/2g * Cc = ((3.14 m/s)^2 - (0.24 m/s)^2)/(2*9.8 m/s^2) * 0.63 = 0.97 m

As we can see, the head loss due to sudden contraction is significantly higher than the loss due to gradual contraction. This is because sudden contraction causes a more abrupt change in velocity, resulting in a larger pressure drop and therefore a higher head loss.

I hope this helps to answer your question! Let me know if you have any further thoughts or questions.