An inviscid incompressible liquid flows steadily from the la

An inviscid, incompressible liquid flows steadily from the large pressurized tank shown in the figure below. The velocity at the exit is 48 ft/s. Determine the specific gravity of the liquid in the tank. First choose an equation to model the flow. Are the assumptions and conditions for the use of Bernoulli\'s Equation satisfied: Can one or more streamlines be identified? Is the flow without significant viscous effects? Is the flow quasi-steady? Is the flow incompressible? Is there any mechanical work done on the fluid?

Solution

a) yes. If laminar flow, the stream lines go thru along the pipe

b) need to know the length of the pipe. Guess is yes

c) yes, after start and before stop, the flow is steady for some time

d) water can be regarded as incompressible under normal conditions

e) there is work done by gravity to change the head before and after.

need to know the density of the liquid to get the velocity. Hence, from Bernoulli

DP/rho +gH = V*V/2

DP = 10psi ( convert to feet*g to fit with the other units given in fps) ie pounds to poundals ( multiply by g=32.2))

rho unknown

g= 32.2 ft/(s*s.)

DImensional analysis

P/rho *g = lb/in^2/lb/in^3 *g= in * in/s^2 = in^2/s^2

gH = in/s^2 * in = in^2/s^2

V^2/2 = (in/s)^2 = in^2/s^2

H = 15ft (at the instant shown)

V = 48 f/s