# Question Video: Calculating Flow Speed through a Pipe Physics • 9th Grade

Some liquid flows inside a pipe with a cross-sectional area of 0.02 m² squared. The liquid flows at 13 kg/s and has a density of 1‎200 kg/m³. Calculate the flow speed through the pipe in meters per second to two decimal places.

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### 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.