Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 month ago

# The rate of flow of a liquid would be measured in units of volume/time (such as the volume of liquid that passes a certain po?

The rate of flow of a liquid would be measured in units of volume/time (such as the volume of liquid that passes a certain point or comes out of a pipe every second).

So the dimensions of the flow rate of a liquid are:

[ flow rate ] = L3 M0 T-1

Jean was doing experiments on the flow rate of water through narrow glass pipes. She noticed that with a pipe that was 10.0 cm long, the flowrate was 0.030 L/s (liters per second). Using the same pressure she tried a pipe with the same radius but a length of 20.0 cm and the flow rate was 0.015 L/s. Using the same pressure she tried a pipe with the same radius but a length of 30.0 cm and found the new flow rate was 0.010 L/s.

The viscosity of water is

vicsosity = 8.9 x 10-4 kg/( s m ) = 8.9E-4 kg/( s m )

The pressure difference between two ends of a water pipe is 1.00 x 104 kg/(s2 m), the radius of the pipe is 1.00 mm. And the length of the pipe is 10.0 cm. Using only dimensional analysis (and what you have learned in this problem) estimate the flow rate of water through the pipe.

For comparison, you might want to know that a detailed calculation shows that the flow rate would be 0.044 L/s. Your estimate should be a little higher, but it should not be off by a factor of 10.