Question

At a soft drink bottling plant, a horizontal section of pipe carrying citric acid in liquid form goes from a cross-sectional area of 8.00 cm2, fluid flow speed of 320 cm/s, and pressure of 1.40 105 Pa to a section of pipe with a cross-sectional area of 3.70 cm2. The density of the citric acid is 1660 kg/m3. For the section of smaller pipe, determine the liquid flow speed and the liquid pressure.

(a) the liquid flow speed m/s
(b) the liquid pressure Pa

Answer 1

a)
`V_2=8m/s`

b)
`P_2=9.54*10^4 Pa`

Step-by-step explanation

From the question we are told that:

Initial Area of pipe
`A_1=8.00 cm^2`

Initial Fluid flow speed
`r_1 =320 cm/s,\approx 320*10^(-2)`

Initial Pressure of
`\rho_1 =1.40*10^5 Pa`

Final area of pipe
`A_2 =3.70 *10^(-2) cm^2`

Density of acid
`\rho=1660kg/m^3`

a)

Generally the equation for continuity is mathematically given by

`A_1V_1=A_2V_2\\\\V_2=(A_1*V_1)/(A_2)`

Since volume is directly proportional to rate of flow

`V_2=(8*320)/(3.20) *10^(-2)`

`V_2=8m/s`

b)

Generally the Bernoulli's equation is mathematically given by

`p_1+(1)/(2)\rho v_1^2+\rho gh_1=P_2+(1)/(2)\rho v_2^2+\rho gh_2\\\\with\ h_1=h_2\\\\p_1+(1)/(2)\rho v_1^2=P_2+(1)/(2)\rho v_2^2`

Therefore

`P_2=P_1+(1)/(2)\rho(v_1^2-V_2^2)\\\\P_2=(1.40*10^5)+(1)/(2)(1660)(v_1^2-V_2^2)`

`P_2=9.54*10^4 Pa`