Torque generated by water flow

[EEristavi]

Homework Statement

Water flows out of a big tank along a tube bent at right angles:
the inside radius of the tube is equal to r = 0.50 cm. The length of the horizontal section of the tube is equal to 1 = 22 cm.
The water flow rate is Q = 0.50 liters per second. Find the moment
of reaction forces of flowing water, acting on the tube's walls, relative
to the point 0 (where tube and tank is connected).

Relevant Equations

## \tau = F R ##
Q = V A

I know that I have to calculate force that is generated by water. However, I do it wrong way.

## A = \pi r^2 ##
## v = \frac Q A = \frac Q {\pi r^2}##
## F = P t = mvt = ...? ## - have problem with mass. and is it even correct way?

if I can calculate F - its easy afterwards...
##\tau = F l ##

P.S.
I looked for the solutions and it says that
## F = (\pi r^2) \rho v^2 ##
I can't get how they wrote it - I tried many approach already..

 

[haruspex]

Consider a small period dt. How much water flows through the bend in that time? What is its mass? What momentum change does it undergo? What is the moment of that about the given point?

By the way, your title does not match your question.

 

[EEristavi]

Consider a small period dt. How much water flows through the bend in that time? What is its mass? What momentum change does it undergo? What is the moment of that about the given point?

when you pointed out in that way (step by step) - light bulb just flashed on :)

Thanks mate!

P.S. I was writing other question other day - forgot to change the title, sorry