Question: ![enter image description here](https://i.stack.imgur.com/TjBvZ.jpg)

Consider the example shown above. Ideal fluid is flowing along the flat tube of uniform cross section area located in the horizontal plane and bent as shown. The flow is steady. My text book says following two things:

1. Pressure at point 1 will be greater than the pressure at point 2 and velocity at point 1 will be less than the velocity at point 2.
2. Streamlines will be higher in density near point 2 than point 1.

I understand that point 1 implies point 2, as velocity is directly proportional to the number of streamlines crossing a unit area.

What I fail to understand are the following points:

1. How do we intuitively understand the idea that pressure at point 1 will be greater than the pressure at point 2?
2. My textbook uses Bernoulli's equation and says that since pressure at point 1 is greater than pressure at point 2, so velocity at point 1 will be less than the velocity at point 2. I completely fail to understand the distribution of velocity at the turning point in the appratus above. Mathematically I am convinced that Bernoulli's equation gives a certain answer but Intuitively I totally fail to understand this answer.
3. Can somebody help me to understand this phenomena just on the basis of forces and not on the basis of Bernoulli's equation?
4. How do we understand the distribution of velocity intuitively?
5. Apart from the bending/turning, in the straight portions, will the streamlines be equidistant? or they will follow the same kind of distribution they are following at the turning? And why? If we assume the streamlines to be equidistant in the straight portions then it means that their distribution changes at the turning point and then again it resets back to what it was earlier, how is this all happening?
6. Can somebody help me to understand the velocity distribution, and the pressure distribution in the above case intuitively, without using Bernoulli's equation?

Thanks in advance.

Answer: 
Laplace's equation in terms of the stream function is based on Euler's equation (which takes into account the inertial forces involved). The solution to Euler's equation will show that the streamlines are closer together at point 2 than at point 1. The pressure has to be higher at point 1 than point 2 because it is on the outside of the curve, so that this region must support the centripetal acceleration of the fluid nearer the center of curvature.
Bennoulis principle has a condition that the flow must be streamline. The curve will create Eddies and Bernoulli's principle will not apply