Please i 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=(0.015/1) + (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.
we know reynold's number= v X D/kinematic viscosity ,
where v =mean velocity,D=diameter of pipe
plug Re in the equation to get f then proceed with Chezy's formula which is C X sq root(Mi)
we know reynold's number= v X D/kinematic viscosity ,
where v =mean velocity,D=diameter of pipe
plug Re in the equation to get f then proceed with Darcy Weisbach formula
To find the headloss due to friction for a length of 10m, we need to calculate the friction factor (f) and the Reynold's number (Re) first. Once we have these values, we can use them to calculate the headloss.
Step 1: Calculate the Reynold's number (Re).
The Reynold's number is a dimensionless quantity used to predict the flow conditions of a fluid. It is given by the formula:
Re = (fluid velocity * hydraulic diameter) / kinematic viscosity.
Given:
- Fluid velocity: 5 m/s
- Pipe diameter: 300 mm = 0.3 m
- Kinematic viscosity of water: 0.01 stoke = 0.01 * 10^(-6) m^2/s (conversion from stoke to m^2/s)
Calculations:
Re = (5 * 0.3) / (0.01 * 10^(-6))
Re = 150,000,000
Step 2: Calculate the friction factor (f).
The friction factor (f) in the given equation is dependent on the Reynold's number (Re) and is represented as:
f = (0.015/1) + (0.08/Re^0.3)
Substitute the value of Re into the equation:
f = (0.015/1) + (0.08/(150,000,000)^0.3)
f = 0.015 + 0.08/(150,000,000)^0.3
Step 3: Calculate the headloss (H) due to friction for a length of 10m.
The headloss due to friction (H) can be calculated using the Darcy-Weisbach equation, which is given by:
H = (f * (L/D) * (v^2/2g))
Given:
- Length of the pipe: 10m (L)
- Diameter of the pipe: 0.3m (D)
- Velocity of the fluid: 5 m/s (v)
- Acceleration due to gravity: 9.81 m/s^2 (g)
Calculations:
H = (f * (L/D) * (v^2/2g))
H = (0.015 + 0.08/(150,000,000)^0.3) * (10/0.3) * (5^2/(2 * 9.81))
Solve the equation to obtain the headloss (H).
Therefore, by following these steps and making the necessary calculations, you can find the headloss due to friction for a length of 10m.