Question

Derive the equation for speed of efflux?

Answer 1

i have pasted 2 links in a notepad, please look

5594048b0cea6d12356d8f8251ba72c4.txt

Answer 2

Answer:

Let A1= area of the slit (it is very small), v1= Velocity with which fluid is flowing out.

A2=Area of the free surface of the fluid,v2=velocity of the fluid at the free surface.

From Equation of Continuity, Av=constant.Therefore A1v1 = A2v2.

From the figure, A2>>>A1, This implies v2<<v1(This meansfluid is at rest on the free surface), Therefore v2~ 0.

Using Bernoulli’s equation,

P+ (1/2) ρ v2+ρgh = constant.

Applying Bernoulli’s equation at the slit:

Pa+(1/2) ρ v12+ρgy1(Equation 1) where Pa=atmospheric pressure,y1=height of the slit from the base.

Applying Bernoulli’s equation at the surface:

P+ρgy2(Equation 2) where as v2=0 therefore (1/2) ρ v12=0, y2=height of the free surface from the base.

By equating(1) and (2),

Pa+ (1/2) ρ v12+ ρgy1= P+ρgy2

(1/2) ρ v12 = (P-Pa) + ρg(y2-y1)

=(P-Pa) ρgh (where h=(y2-y1))

v12=2/ρ [(P-Pa) + ρgh]

Therefore v1=√2/ρ [(P-Pa) + ρgh].This is the velocity by which the fluid will come out of the small slit.

v1 is known as Speed of Efflux. This means the speed of the fluid outflow.