Chapter 7, Problem 31RQ

We wish to analyze the velocity of a fluid exiting from an orifice in the side of a pressurized tank. Examine the equations below using fundamental dimensions and indicate for each if the equation is a valid or invalid equation; justify your answer for each case.

a. $v=\frac{p}{\rho }+\sqrt{2gH}$

b. $v=\sqrt{\frac{P}{\rho }+2H}$

C. $v=\sqrt{\frac{2P}{\rho }+2gH}$

d. $v=\sqrt{2p+2gH}$

Here, the variables are as follows:

g = gravity [=] m/s²

H = height or depth of the fluid [=] ft

P = pressure[=] atm

v = velocity [=] ft/min

ρ = density [=] kg/m³