please solve the following question Water flows through a c

please solve the following question ..

Water flows through a constricted pipe at a uniform rate. At one point, the diameter of the pipe is 0.08 m and the pressure is 3 times 10^4 N/m^2. At another point, 0.5 m higher than the previous point, the diameter is 0.04 m and the pressure is 1.5 times 10^4 N/m^2. Calculate the velocities at the lower section and the upper section as well as the rate of the flow.

Solution

From Continuity equation

A₁V₁=A₂V₂

=>(pi*0.08²/4)*V₁ =(pi*0.04²/4)*V₂

V₂=4V₁

From Bernoulli\'s equation

P₁+(1/2)pV₁²+pgh₁ = P₂+(1/2)pV₂²+pgh₂

(3*10⁴)+(1/2)*1000*V₁² +1000*9.8*0 = 1.5*10⁴+(1/2)*1000*(4V₁)²+1000*9.8*0.5

15V₁²=20.2

V₁=1.16 m/s (Lower section)

and V₂=4*1.16

V₂=4.64 m/s(upper section)

Flow rate

Q=A₁V₁ = (pi*0.08²/4)*1.16

Q=0.00583 m³/s