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
1/r5
1/r3
1/r4
1/r
Answer: Option
Explanation:
No answer description is available. Let's discuss.
Discussion:
27 comments Page 1 of 3.

Desalegn Degu said:   5 years ago
For this
a = V^2/r.

Here, V = 1/r^2 hence,
a = [(1/r^2)^2]/r,
= (1/r^4)/r.

a = 1/r^5.
(8)

Phani said:   6 years ago
Simple V = d/t,

Given V = 1/r^2 and d = r,
Substitute t = r^3,
Now a = V/t = 1/r^5.
(7)

Gourab said:   3 years ago
a= v(dv/ds) + dv/dt

As steady flow is taking place, dv/dt=0.
a= v (dv/ds).
now, v= k/r2.
dv/ds= dv/dr= -2k/ r3.
therefore, a varies as 1/r5.
(1)

Blackie said:   3 years ago
Yes, 1/r5 is correct.
(1)

Aki said:   5 years ago
Well explained, Thanks @Desalegn Degu.
(1)

Niki said:   6 years ago
I agree @Maha.
(1)

Kumari juhi said:   7 years ago
a = V2/r = (1/r2)2/r = 1/r5.

Maha said:   6 years ago
Thanks for explaining the answer.

Nanu said:   6 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).

M.naresh said:   6 years ago
We know the radial acc is=V2/r .(1/(r2)2*r=1/r5.


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