Best products from r/FluidMechanics

Fluid Mechanics 4th Edition by Kundu (A good graduate level text. The practice problems are really great and challenging. The 5th edition has better practice problems, but the layout and content of the 4th is better IMO.)

Elementary Fluid Dynamics by Achenson (Good graduate level text with mathematical rigor.)

Fluid Mechanics by Granger (A good undergraduate level text.)

An Introduction to Fluid Dynamics by Batchelor (This one is much more advanced than the rest.)

Check DJ Tritton, Physical Fluid Dynamics. Written by an experimentalist , it's great for developing intuition.

https://www.amazon.in/dp/0198544936/ref=cm_sw_r_cp_awdb_t1_nkNrDbSVMW9YZ

Chapter one of a different Anderson book, Introduction to Flight has a good overview of the history. He also wrote a book just on history of aerodynamics that might be more useful to you.

I can recommend the book "Flow: Nature's Patterns: A Tapestry in Three Parts", I found it on a liberary or you can find it on amazon here: https://www.amazon.com/Flow-Natures-Patterns-Tapestry-Three/dp/0199604878

It is fairly short and has no equations iirc while still covering a lot of different type of flows and in an interesting way.

https://www.amazon.com/Introduction-Magnetohydrodynamics-Cambridge-Applied-Mathematics/dp/0521794870 I'm taking a look on this one and enjoying it thus far

Equations and relevant info you're asking for is contained in Engineers Practical Databook including the equations for pipe flow, and K factors to get the pressure drop across a variety of types of valve. I have shared a summary review of this problem which I wrote during my Masters degree in fluids class here, on 'experimental studies on transition to turbulence in a pipe'.

Reynold's Number
Firstly, to understand flow through a pipe you absolutely need to know what the Reynolds Number is. The number is calculated using Re = ρvD/μ where
ρ is density of the fluid, or 998 kg/m^3 for water around 20°C.
v [m/s] is velocity of the fluid.
D [m] is diameter of the pipe.
μ is the dynamic viscosity of water, or 1.00x10^-4 [Pa.S] at 20°C.

This is a dimensionless number (no units). Below about 2,000 the flow is laminar and above about 3,000 the flow is usually turbulent, and in between it may be transitioning. Laminar flow is steady (with time) and is associated with less wasted energy, faster flowrates, and less drag. Turbulent flow is unsteady, has lots of shearing, mixing and energy dissipation. See image.

If the flow is turbulent, stop here. I studied turbulence as a graduate student and must say it's tricky and a lot relies on empirical (experimental) factors. Unless you're working towards a physics or engineering Masters/PhD, it's not something you'd likely go into much detail on. If you want to know about your flow, just find a way to physically measure it.

But if your flow is laminar, proceed.

Velocity
To understand velocity through a pipe for laminar flow, first we know that the velocity is zero at the walls due to the 'no-slip condition'. Then due to symmetry the flow is fastest in the centre, furthest from the walls. We assume the velocity is parabolic and axi-symmetric, i.e. in cylindrical coordinates, v_r = v_max*[1-(r^2 / R^2 )
where
v_r [m/s] is the velocity at radius r [m] from the centre.
v_max [m/s] is the velocity at the centre.
r [m] is the distance from the centreline.
R is the radius of the pipe.

Flow Rate
If the flow is laminar you can calculate the flow rate Q or the pressure drop ΔP using the Hagen–Poiseuille equation. You will find in the equation an f or a lambda in the aforementioned book which represents the roughness of a pipe, usually on the order of microns average surface roughness. There is an additional pressure drop across a valve which is represented as a K-factor. The databook has K-factors for a variety of valves, and you can find these online also. Or see the paper I linked at the top, I put in an example.

If you know what the flowrate or velocity is at any point in a pipe, and the flow is steady (unchanging with time), you can easily calculate the velocity anywhere else using conservation of mass from point 1 to point 2: Flowrate in = Flowrate out, or ρ_1 v_1 A_1 = ρ_2 v_2 A_2. For constant density (i.e. near constant temperature water) then use v_1 A_1 = v_2 A_2. The velocity x area going in is the velocity x area out of a pipe.

Pressure
The equation for pressure drop is given along a streamline using Bernoulli's equation, where the three terms (static pressure + dynamic pressure + gravitational specific energy) is constant at any points along the streamline. If you know the height and the velocity between two points, you can work out the pressure change P_2 - P_1.

P_1 + 1/2 (ρ_1)(v_1)^2 + (ρ_1)(g)(h_1) = P_2 + 1/2 (ρ_2)*(v_2)^2 + (ρ_2)*(g)*(h_2).
where
P is the static pressure in [Pa] or [N/m^2 ].
ρ [kg/m^3 ] is density.
v [m/s] is velocity.
g is acceleration due to gravity, defined as 9.80665 [m/s^2 ].
h [m] is vertical height above a datum.

The Bernoulli equation, like many things, does not work when the flow is unsteady, or rotational, or when the fluid gets compressed, or when viscosity is important. In other words, nothing is easy when things are turbulent.