If a pipe is subject to a wide range of temperatures, the stress, lb/in² (MPa), due to a temperature change is
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The internal or external pressures on the pipe walls cause the stresses acting perpendicular to the longitudinal axis of a pipe.
Internal pressure creates a stress commonly called hoop tension

The sum of the forces in the horizontal direction is

pD=2F

where
p= internal pressure, lb/in² (MPa)

D= outside diameter of pipe, in (mm)

F= force acting on each cut of edge of pipe, lb (N)

Hence, the stress, lb/in² (MPa) on the pipe material is

pD=F/A= pD/2t

where
A= area of cut edge of pipe, ft² (m²)
t= thickness of pipe wall, in (mm).

Water hammer is a change in pressure, either above or below the normal pressure, caused by a variation of the flow rate in a pipe.

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This type of tube can greatly increase the flow through an orifice by reducing the pressure at the orifice below atmospheric. The formula that follows for the pressure at the entrance to the tube is obtained by writing the Bernoulli equation for points 1 and 3 and points 1 and 2

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Where the effect of air resistance is small, the path of projectile is followed when a fluid discharged through an orifice into the air
The initial velocity of the jet is

V₀ = C_v?2gh

where h= head on center line of orifice, ft (m),
C_v =coefficient of velocity.

The direction of the initial velocity depends on the orientation of the surface in which the orifice is located.The velocity of the jet in the X direction (horizontal) remains constant

V_x = V₀ = Cv ?2gh

The velocity in the Y direction is initially zero and there after a function of time and the acceleration of gravity:

V_y = gt

The X coordinate at time t is
X = V_x t = tC_v ?2gh

The Y coordinate is

Y = V_avg t= gt²/2

where V_avg =average velocity over period of time t.

The equation for the path of the jet:

X₂ = C_v* C_v *4hY