Civil Engineering - Hydraulics - Discussion

A is correct answer.

Reason behind that v^2/2g is a term used in specific energy not for critical depth i.e. E= h+v^2/2g = specific energy.

But critical depth is that depth at which specific energy is minimum so we have to differentiate above equation w.r.t h ... And then term comes dE/dh= 1+ q^2/2g(-2/h^3)=0 ... And simplify this equating we will get h= q^2/g .... i.e. (av)^2/g... i.e. v^2/g.

I hope you will understand what i m saying good luck friends for your future.

The depth of water in a channel when vel of flow is critical or when the specific energy is min is called critical depth of the channel.

Critical vel of flow is the vel at which sp.energy is minimum.
Specific energy -> E=h+(v^2/2g).
For minimization, dE/dh =0.
On putting v=Q/A.
We get , 1=v^2/gh.
So, V= (gh)^1/2 or sqrt of gh.

Which is critical velocity;
So, critical depth= v^2/g.

As per Froude Number (Fr):

If Fr < 1 then flow is Sub-Critical flow.
If Fr > 1 then flow is Super-Critical flow,
If Fr = 1 then flow is Critical flow,

So, The formula of Fr is:
Fr = v / ( g d) ^ 1/2.
For critical depth put Fr = 1 and solve for d.
1 = v / ( g d) ^ 1/2,
(g d) ^1/2 = v.

Squaring on Both Sides;
(g d) = v ^2.
d (critical) = (v ^2)/g.

Froudes number= Inertia Force/viscous force.

F= V/(gy)^0.5.
For channel flow to be critical (Fr=1).
Now, 1= V/(gy)^0.5.

=>. (gy)^0.5 = V
=>. gy = V^2
=>. y= V^2/g.

Thus, Option A is correct.

As it depends on froudes number. For critical flow froudes number is one and the depth corresponding to critical flow is called critical depth.

Froudes number = Velocity/Root of height*velocity.

For critical depth = v/root of height * gravity.
1 = v/root of height * gravity,
The root of height * gravity = v,
Taking square of both side.
h * g = v^2
h = v^/g.

For critical flow type specific energy = yc + v2/2g.
for rectangular channel = Ec = 1.5 yc.
1.5 yc = yc + v2/2g,
0.5 yc = v2/2g,
yc = v2/g.

E = y + v^2/2g is specific energy.
Here, v^2/2g is KINETIC energy and "y" is POTENTIAL energy.
So, the given answer is correct.

hc=( q2/g)^1/3.

Taking cube on both sides hc^3= q2/g.

q=Q/b= A*V/b= (b*h*V)/b= (h*v),
hc^3= (hc * V)^2/g,
hc= V2/g.

V in the above equation is critical velocity. That is velocity with respect to the critical depth of flow.