Water is flowing in a pipe with a varying cross-section area, and at all points the water completely fills the pipe. At point 1 the cross-section area of the pipe is 0.080 m^2, and the magnitude of the fluid velocity is 2.50m/s. Calculate the volume of the water discharged from the open end of the pipe in 1 second.
For incompressible fluids in steady state flow, the volume rate of flow is constant along the flow direction. What goes in must come out at the same rate, in volume per second. This is called the "continuity equation".
Therefore
A* V = 0.08 * 2.50 = 0.20 m^3/s
is the volume flow rate at the discharge end, and everywhere else.
Well, if the water completely fills the pipe at all points, then it must be dreaming of becoming a solid pipe. Talk about pipe dreams!
Now, to calculate the volume of water discharged from the open end of the pipe in 1 second, we need to use the equation:
Volume = Area * Velocity * Time
Here, the area at point 1 is given as 0.080 m^2, so let's plug in the values:
Volume = 0.080 m^2 * 2.50 m/s * 1 s
And after a brief calculation, we find that:
Volume = 0.20 cubic meters
So, the volume of water discharged from the open end of the pipe in 1 second is 0.20 cubic meters. That's enough water to make a small kiddie pool!
To calculate the volume of water discharged from the open end of the pipe in 1 second, we need to determine the volume flow rate and then multiply it by the time.
The volume flow rate is given by the equation:
Q = A * V
where:
Q is the volume flow rate,
A is the cross-section area of the pipe, and
V is the fluid velocity.
From the given information:
A = 0.080 m^2
V = 2.50 m/s
Let's substitute these values into the equation:
Q = 0.080 m^2 * 2.50 m/s
Q = 0.20 m^3/s
The volume flow rate is 0.20 cubic meters per second.
To find the volume of water discharged in 1 second, we multiply the volume flow rate by the time:
Volume = Q * time
Volume = 0.20 m^3/s * 1 s
Volume = 0.20 m^3
Therefore, the volume of water discharged from the open end of the pipe in 1 second is 0.20 cubic meters.
To calculate the volume of water discharged from the open end of the pipe in 1 second, you need to first determine the volume flow rate of the water through the pipe. The volume flow rate is the product of the cross-sectional area and the fluid velocity.
Given:
Cross-sectional area at point 1 (A1) = 0.080 m^2
Fluid velocity at point 1 (v1) = 2.50 m/s
To find the volume flow rate (Q), you can use the equation:
Q = A1 * v1
Substituting the values given:
Q = 0.080 m^2 * 2.50 m/s
Q = 0.200 m^3/s
The volume flow rate is 0.200 cubic meters per second.
To find the volume of water discharged from the open end of the pipe in 1 second, you can multiply the volume flow rate by the time (t). In this case, the time is 1 second.
Volume of water discharged = Q * t
Volume of water discharged = 0.200 m^3/s * 1 s
Volume of water discharged = 0.200 m^3
Therefore, the volume of water discharged from the open end of the pipe in 1 second is 0.200 cubic meters.