Pls...,need help.
QUESTION=Water flows through a pipe of diameter 300mm with a velocity of 5m/s.if the coefficient of friction is given by f=(0.015)+(0.08/Re^0.3)
where Re is the Reynoid number.
Take kinematic viscosity of water as 0.01stoke.
*Find the headloss due to friction for a length of 10m
To solve this problem, you need to calculate the Reynold's number using the given data and then use it to find the headloss due to friction. Here's how you can do it step by step:
1. Calculate the Reynold's number (Re):
The formula for the Reynold's number is Re = (ρ * v * D) / μ, where
- ρ is the density of the fluid (water in this case),
- v is the velocity of the fluid (given as 5 m/s),
- D is the diameter of the pipe (converted to meters, which is 0.3 m), and
- μ is the kinematic viscosity of water (given as 0.01 stoke).
Plugging in the values:
Re = (ρ * v * D) / μ = (1000 kg/m^3 * 5 m/s * 0.3 m) / (0.01 stoke)
2. Convert the kinematic viscosity from stoke to m^2/s:
1 stoke = 0.0001 m^2/s
So, μ = 0.01 stoke * 0.0001 m^2/s = 0.000001 m^2/s
3. Plugging in the values into the Reynold's number equation:
Re = (1000 kg/m^3 * 5 m/s * 0.3 m) / (0.000001 m^2/s)
Calculate the value of Re.
4. Using the value of Re, calculate the coefficient of friction (f):
Given f = (0.015) + (0.08 / Re^0.3)
Substitute the value of Re into this equation and calculate f.
5. To find the headloss due to friction (h) for a length of 10 m, use the Darcy-Weisbach equation:
h = f * (L / D) * (v^2 / (2 * g))
Where:
- f is the coefficient of friction calculated in step 4,
- L is the length of the pipe (given as 10 m),
- D is the diameter of the pipe (given as 0.3 m),
- v is the velocity of the fluid (given as 5 m/s), and
- g is the acceleration due to gravity (approximately 9.81 m/s^2).
Plug in the values and calculate h.
That's how you can find the headloss due to friction for a length of 10 m using the given data and formulas.