Question

A 100-mm pipe is used to transfer oil from a reservoir to a 100- liter tank. It takes 45 minutes to fill the tank with oil that has viscosity and density of 0.005 Pas and 900 kg/m3, respectively Determine a. The volume flow rate of oil b. Mean velocity in the pipe; c. Reynolds number, and d. The maximum velocity in the pipe

Answer 1

Step-by-step explanation:

Given that,

Diameter =100 mm

Volume = 100 liter

Time = 45 min

Viscosity = 0.005 Pas

Density = 900 kg/m³

(a). We need to calculate the volume flow rate of oil

Using formula of flow rate

`q=(V)/(t)`

Put the value into the formula

`Q=(0.1)/(2700)`

`Q=3.7*10^(-5)\ m^3/s`

The volume flow rate of oil is
`3.7*10^(-5)\ m^3/s`

(b). We need to calculate the mean velocity in the pipe

Using formula of mean velocity

`v=(Q)/(A)`

`v=(Q)/((\pi)/(4)* d^2)`

Put the value into the formula

`v=(3.7*10^(-5))/((\pi)/(4)*(100*10^(-3))^2)`

`v=4.7*10^(-3)\ m/s`

The mean velocity in the pipe is
`4.7*10^(-3)\ m/s`.

(c). We need to calculate the Reynolds number

Using formula of the Reynolds number

`R_(e)=(\rho v d)/(\mu)`

Put the value in to the formula

`R_(e)=(900*4.7*10^(-3)*100*10^(-3))/(0.005)`

`R_(e)=84.6`

The Reynolds number is 84.6.

(d). We need to calculate the maximum velocity in the pipe

Using formula of maximum velocity

`V_(max)=2v_(avg)`

Put the value into the formula

`v_(max)=2*4.7*10^(-3)`

`v_(max)=9.4*10^(-3)\ m/s`

The maximum velocity in the pipe is
`9.4*10^(-3)\ m/s`

Hence, This is the required solution