Video Transcript
Some liquid flows inside a pipe
with a cross-sectional area of 0.02 meter squared. The liquid flows at 13 kilograms
per second and has a density of 1200 kilograms per meter cubed. Calculate the flow speed through
the pipe in meters per second to two decimal places.
In this question, we want to
calculate the flow speed of the liquid through the pipe. Let’s begin by visualizing the
problem. We can recall the mass flow rate of
a fluid flowing through a pipe is given by the equation 𝑚 over 𝑇 equals 𝜌𝐴𝑣,
where 𝑚 is the mass of the fluid passing through a cross section of the pipe. 𝑇 is the time the cross section is
measured for. 𝜌 is the density of the fluid, 𝐴
is the cross-sectional area of the pipe. And 𝑣 is the velocity of the
fluid.
We want to calculate the flow speed
through the pipe. So we want to make 𝑣 the
subject. We can do this by dividing both
sides of the equation by 𝜌𝐴, to leave us with 𝑣 equals 𝑚 over 𝑇𝜌𝐴. In the question, we are told that
the liquid flows at 13 kilograms per second. This is the mass flow rate 𝑚 over
𝑇. So 𝑚 over 𝑇 equals 13 kilograms
per second. We are also given the density of
the liquid, which is equal to 1200 kilograms per meter cubed, and the
cross-sectional area of the pipe, which is equal to 0.02 meters squared.
Substituting these values into our
equation, we find that the flow speed through the pipe 𝑣 is equal to 13 kilograms
per second over 1200 kilograms per meter cubed multiplied by 0.02 meters
squared. Looking at our units, the kilograms
in the numerator will cancel with the kilograms on the denominator. The “per meters cubed” in the
denominator will end up on the numerator. And so meters cubed over meters
squared will leave us with meters. And so, we are left with meters in
the numerator and seconds in the denominator. Therefore, our answer will be in
meters per second.
Completing the calculation, we get
a value of 0.54 meters per second to two decimal places. And this is our answer. The flow speed through the pipe is
equal to 0.54 meters per second.
