- #1

member 428835

## Homework Statement

I am happy to re-write the question, but I'm just leisurely working through a list of problems I found online, so here is the link (with picture).

http://web.mit.edu/2.25/www/5_pdf/5_01.pdf

## Homework Equations

Cons of Momentum

Cons of Mass

## The Attempt at a Solution

a) I would use Bernoulli's equation since flow is inviscid and incompressible and conservation of mass. Steady flow implies Bernoulli's equation is ##P_1+1/2 \rho V_1 = P_A+1/2 \rho V_2## and Conservation of mass is ## R_1^2 V_1 = R_2^2 V_2##. Thus we may solve for and know ##P_1##.

b) Take a CV to be the fluid in the nozzle, starting somewhere at ##R_1## and ending at ##R_2##. Since we only consider this force during steady flow, conservation of momentum is $$\iint \rho \vec{V} (\vec{V_{rel}}\cdot \vec{n})\,dA = \sum \vec{F} \implies\\ -\rho V_1^2 \pi R_1^2+\rho V_2^2 \pi R_2^2 = -P_1 \pi R_1^2+P_a \pi R_2^2 +\vec{F_{bolt}}$$

Does this look correct? If so, what would change if we didn't have the bolt, but rather the pipe was manufactured with the nozzle directly apart of itself? The tensile force ##\vec{F_{bolt}}## wouldn't be in the equation, but surely the force would not simply be gone, right?

Thanks!