Civil Engineering - GATE Exam Questions - Discussion
Discussion Forum : GATE Exam Questions - Section 1 (Q.No. 5)
5.
In a steady radial flow into an intake, the velocity is found to vary as (1/r2), where r is the radial distance. The acceleration of the flow is proportional to
Discussion:
27 comments Page 2 of 3.
Chandra said:
1 decade ago
I cannot understand this concept. Can anybody elaborate me please?
Aparna said:
10 years ago
v2/r but; v = 1/r2 so v = 1/r4+1; v = 1/r5.
Maha said:
7 years ago
Thanks for explaining the answer.
Yoga said:
10 years ago
Acceleration a = V2/r = (1/r2)2/r = 1/r5.
Nanu said:
7 years ago
dr/dt = - constant / r*r.
To find the acceleration, we want to differentiate the velocity with respect to time. That is:
a = d/dt(dr/dt). = - constant * d/dt(1/r*r)
Now, if f is a function of r, then d/dt(f) = df/dr * dr/dt and so;
a = - constant * d/dt(1/r*r) = - constant * ( -2 / r*r*r) * (-constant) / r*r.
a = -2 * velocity^2 / r = - 2 * constant^2 / r*r*r*r*r.
So the acceleration is proportional to 1 / (r*r*r*r*r).
To find the acceleration, we want to differentiate the velocity with respect to time. That is:
a = d/dt(dr/dt). = - constant * d/dt(1/r*r)
Now, if f is a function of r, then d/dt(f) = df/dr * dr/dt and so;
a = - constant * d/dt(1/r*r) = - constant * ( -2 / r*r*r) * (-constant) / r*r.
a = -2 * velocity^2 / r = - 2 * constant^2 / r*r*r*r*r.
So the acceleration is proportional to 1 / (r*r*r*r*r).
Deepak said:
9 years ago
I agree with you @Aparna.
M.naresh said:
8 years ago
We know the radial acc is=V2/r .(1/(r2)2*r=1/r5.
TEJA said:
9 years ago
Nice @Aparna.
Maha said:
8 years ago
For radial flow,
a = V^2/r.
Here, V = 1/r^2 hence,
a = [(1/r^2)^2]/r,
= (1/r^4)/r,
a = 1/r^5.
a = V^2/r.
Here, V = 1/r^2 hence,
a = [(1/r^2)^2]/r,
= (1/r^4)/r,
a = 1/r^5.
DEEPANCHAKARAVARTHY said:
8 years ago
Thanks @Aparna.
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