# Resultant force - Fluid Dynamics vs Fluid Statics pipe bend vs thrust force

After looking at a few examples between fluid statics and dynamics I am interested to know where the resultant force would be in the following example.

A straight hose of infinite length containing a pressure flow is pricked by a pin causing a leak- the angle of the hole causes the fluid to be ejected in the opposite direction of the main flow . Would the resultant force be in front of the hole (Green) as suggested by Fluid dynamics pipe bend control volumes ( if we considered the pin prick an extremely small pipe turning the main fluid flow past 90') or on the opposite side of the hose (Red) as suggested by thrust vector examples in statics. What confuses me is while there is a flow the hole should only 'see' the static pressure. I imagine both could be correct given the size of hole? Is the difference whether the boundary layer is maintained over the hole?

• The resultant force on what? – Chet Miller Feb 5 at 13:29
• @ChesterMiller I imagine that it would have to be the hose body? – Tom Chester Feb 5 at 19:05
• Is there a reason that you feel that the macroscopic (control volume) momentum balance in combination with the Bernoulli equation gives the wrong answer for the net force exerted by hose on the fluid (and consequently, from Newton's 3rd law, the net force exerted by the fluid on the hose)? – Chet Miller Feb 6 at 0:34
• @ChesterMiller I guess my confusion is why the momentum balance would give a different answer as the dynamic pressure should play no part shouldn't it be the same as a static fluid of the same static pressure escaping?. A static fluid escaping a hole in the bottom of a bucket would give a resultant force on the opposite side of the bucket. I'm trying to understand if the angle of the 'hole' deflects the flow or that the line of thrust corresponds with the opposite of the fluid acceleration. – Tom Chester Feb 6 at 0:52
• I don't follow. Can you please give the development solving it the two different ways in detail? – Chet Miller Feb 6 at 1:17