Clarification on circular motion and pseudo-forces The way i interpret pseudo-forces is that its a mathematical correction that makes the conclusion of the observer in an accelerated frame correct.
And I also believe that this "pseudo-force" has no physical significance, that is, it isn't something actually acting on the body being observed.
While doing circular motion problems, while analyzing from the rotating frame, we add a pseudo-force in the outward direction.
Now, we *actually do feel an outward force * when we are in circular motion, (like when we are taking a turn on the road) and I have seen many textbooks attributing this to the "centrifugal force", which I believed to be simply a pseudo-force and thus, is not something that is physically affecting a body.
What is the correct explanation to this problem?
edit: I think I somewhat got the idea, but I still don't feel I can generalize it to other situations, like:
1)A liquid in a rotating tube (in a horizontal plane) moves Outwards
2)Suppose a block is kept on a rough rotating table,(the block also rotates).We say that friction provides the centripetal force.
But say the angular speed is such that friction becomes insufficient to provide the force, and the block moves outwards. Also, from an inertial frame, if friction is acting towards the center, it means the body has a tendency to move away from the center.
Can these two situations be explained by the same, inertia arguement?
 A: You are correct that pseudo-forces can be viewed as a mathematical correction to allow for Newton's second law to work in non-inertial reference frames, and I tend to think of it as such most of the time. However, really these pseudoforces are the effects of inertia. They aren't forces, but they still are a property of matter.
I would argue then that you really do "feel" pseudoforces due to your own inertia. You have already given the example of circular motion. Another example is when you go upward in an elevator you feel heavier for a little bit, and then when the elevator slows down you feel lighter for a little bit. Sure these effects are not forces (as they do not follow Newton's third law), but they still are "real" in terms of they arise from something physical.
I don't think there is any law saying forces are the only thing you can "feel". Especially if your body is actually in a non-inertial frame of reference.
A: You actually don't feel any such outward force.
Remove the car from the scenario, and you will realise that you are in fact not pushed outwards, but just continuing straight ahead. The car is pulled in so it turns, but you aren't. In other words: 


*

*the car is moving away from underneath you, not you moving away from it.

*And the car window is moving into you, not you squeezing into it.


You are the object that just tries to continue straight ahead, while the car is the object which is changing its course, its velocity, due to a force acting on it. There is no force acting on you.
But when you are sitting in the car, your brain adopts the perspective - the reference frame - of the car. That's a trick of our minds. An illusion like any other optical illusion. When the car turns away from underneath you, your brain doesn't realise that it is the car which is moving away from you. Instead, the brain assumes that surely the car is fixed/non-accelerating and thus it must be you who is moving away from the car.
This non-existing force that would have been pushing you outwards is indeed non-existing but fictitious and what we call a pseudo-force. True, if we do consider an accelerating frame of reference, such as that of the car, then these illusions do play a role and we must then involve such pseudo-forces to make the math - to make Newton's laws e.g. - hold true. If you stick to inertial frames, then you never need them.
A: The force you feel, for example when you take a turn, is the result of your body trying to move in a straight line and the car pushing you in some other direction. Hence the true force comes from the car acting on your body.
The term "pseudo" results from the fact that the force you seem to be feeling is the opposite of the true force, her being the centripetal force induced by friction etc. So in some sense the centrifugal force is still physical, it is just not the "true" force as observed from an inertial frame of reference.
A: Yes, many people have some issues with this. Centrifugal force is a pseudoforce in the same way that a force that is slaming you into a seat of a car is a pseudoforce. It is true that there is no outsiede sources for these pseudoforces but there is one intrinsic and that is your inertia. That is why many people call these forces inertial. So when something is trying to keep you on a circular path it has to apply force on you to keep changing your direction. Your body wants to move uniformly in a definite direction so when something is trying to change its direction your body fights back id est, it oposes the change in motion. Now, if you are on some chain, you will feel some force trying to pull you away from the center but this is actually your body resisting the change in direction of its movement. When we model such situations we imagine a force called centrifugal just to make it easier to calculate.
A: 
Now, we *actually do feel an outward force * when we are in circular
  motion, (like when we are taking a turn on the road) and I have seen
  many textbooks attributing this to the "centrifugal force"

There are a  number of good answers here. Each gives a slightly different flavor to the same phenomenon. This is another "flavor". Judge which works best for you.
If you are the driver, the true, or contact force you actually "feel", is the force your seat or the driver side door is applying to you, which is the true, or centripetal, force that pulls you inward toward the center of the circular path of the car. If it were not for the centripetal force your motion would be uniform and in a straight line relative to the road because of your inertia and Newton's first law. The pseudo, or centrifugal force, is what you think is pushing you in the opposite direction (outward from the turn) although nothing is actually making physical contact with you.
Perhaps a more straight forward example (no pun intended) of a pseudo force is one that is not a centripetal force. It is the one you feel when you accelerate or brake your car. 
Take the case of acceleration. You feel like something is pushing you back against your seat. But there is no contact force against your chest. That is the pseudo force. It reflects your inertia, or resistance to change in motion, due to Newton's first law.  The true force is the contact force of the seat pushing you forward which is transmitted from the car to you giving you an acceleration with respect to the inertial frame of the road. 
Hope this helps.
A: As stated in other answers: we all agree that inertia is a physical thing.
As you point out, when you are in car making a turn you feel the car making that turn.
To lay out the properties of that physical sensation I'm going discuss first how our sensation of gravity comes about. 
As we know, gravity pulls on all the parts of your body equally. That is, the way gravity acts is completely distributed. Let's say you are standing up. The effect from gravity that you actually feel is a sense of compression of your body along the direction of gravity. The sensation of compression is the strongest for the soles of your feet, obviously. The soles of your feet are the only part of your body that is in contact with the ground, so all of your body weight presses on that area.
From there you can go up the length of your body; every part of your body has to support the weight of the parts above it, but not the parts under it; the sensation of compression becomes less and less the higher up.
Without any thinking we know where that sensation of compression is coming from: gravity!
Since there is never a moment you are not subject to gravity this attribution to gravity is among the most automated of our perceptions. 
Inertia
Now compare the case of gravity with the effect from inertia that you experience when you are in a car that is making a turn. First, all parts of your body are equally subject to inertia. That is, the way inertia acts is completely distributed. 
Let's say your shoulder is against the door of the car. The car is making such a sharp turn that the door has to push pretty hard against you to make your body follow that curve. Let's say your arm is along your torso, so it's between your torso and the door. The sensation in your arm is then one of compression; your arm is a bit squeezed between the door and your torso. You feel compression of your body, identical to what you feel when you are laying on your side.
We have that the sensation of compression in your body that you feel (as the car makes a turn) is identical to the sensation of compression from gravity (when you are laying on your side.)
Automatically you attribute that sensation of compression to a gravity-like force, acting outward. 
The attribution happens so automatically that you aren't even aware that you are making an inference. 
Going back to gravity for a little bit. When you think about it: we actually don't feel gravity directly. Gravity has an effect, you have sensation of compression. But we don't think of gravity by its effect. Instead we automatically, without any thinking, correctly infer the cause: a gravitational force. For gravity: having that perception completely automated is good thing, you are never in a situation where you are not subject to gravity.
In the case of the example of a car making a turn, we feel the compression as the door pushes against our body and automatically, without any thinking, we infer a causal force: a centrifugal force.
A: If a body or an object is moving in circular motion, centrifugal and centripetal force acts which is generally pseudo forces. These pseudo forces acts on a body to balance with another contact force or other force in order to move in a circular motion. 
