Lubricating oil, with a relative density of 0.79, flows around a 90º bend. The pipe diameter is 0.45m, and the oil has a pressure head of 7m and the flow is 1.7m3/s. Find the force exerted by the oil on the bend.
density = .79 * 10^3 kg/m^3
velocity of oil = v
v*pi r^2 = 1.7
v =1.7 /(pi*.45^2) = 2.67 m/s
x momentum of oil coming down the pipe = m v = 1*2.67 = m 2.67 m/s
Since the oil turns 90 degrees, the x momentum out is zero
so
what is the change of momentum per second (the force)?
mass per second = .79*10^3 kg/m^3 * 1.7 m^3/s
= 1343 kg/s
so force due to change of momentum/second = 1343 kg/s*2.67 m/s
= 3586 Newtons
Now add to that the pressure times the area of the pipe for the x component of pressure force.
Note there is a similar y force.
Thank you, makes so much sence now! lol :-)
To find the force exerted by the oil on the bend, we need to consider the momentum change of the fluid as it flows through the bend.
First, we need to find the velocity of the fluid at the entrance and exit of the bend.
The velocity of the fluid can be calculated using the equation:
v = Q / A
Where:
v = velocity of the fluid
Q = flow rate of the fluid
A = cross-sectional area of the pipe
Given:
Q = 1.7 m^3/s
A = (π * D^2) / 4, with D = 0.45 m (pipe diameter)
Calculating the area:
A = (π * 0.45^2) / 4
A = 0.159 m^2
Calculating the velocity at the entrance and exit of the bend:
v_entrance = Q / A
v_entrance = 1.7 / 0.159
v_entrance ≈ 10.693 m/s
v_exit = Q / A
v_exit = 1.7 / 0.159
v_exit ≈ 10.693 m/s
Since the velocity is the same at the entrance and exit, there is no change in velocity. Therefore, there is no momentum change in the direction of flow.
Next, we need to consider the change in pressure head of the fluid as it flows around the bend.
The change in pressure head can be calculated using the equation:
ΔP = ρ * g * h
Where:
ΔP = change in pressure head
ρ = density of the fluid
g = acceleration due to gravity
h = height or pressure head
Given:
ρ = relative density = 0.79
g = acceleration due to gravity = 9.8 m/s^2
h = pressure head = 7 m
Calculating the change in pressure head:
ΔP = ρ * g * h
ΔP = 0.79 * 9.8 * 7
ΔP ≈ 54.976 Pa
Now, we can calculate the force exerted by the oil on the bend.
The force can be calculated using the equation:
F = ΔP * A
Where:
F = force exerted by the fluid
A = cross-sectional area of the pipe
Calculating the force:
F = ΔP * A
F = 54.976 * 0.159
F ≈ 8.748 N
Therefore, the force exerted by the oil on the bend is approximately 8.748 N.