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Intro - Density - Pressure - Depth - Pascal - Archimedes - Continuity - Bernoulli - Solutions

Equation of Continuity

      You probably have experienced that if you place your thumb over the end of a garden hose that you can make the water spray out at a higher velocity. This can be described by the equation of continuity which says that the area through which a fluid is flowing and the velocity of the fluid are inversely related. This equation can be written as:

A1v1 = A2v2

where A is the area of the hose in meters2 and v is the velocity of the fluid in meters. Therefore, Av equals what is called the volume flow rate (Q) and has the units m3/s. In general, as seen below, a fluid flowing in a tube that has different cross-sectional areas A1 and A2 at positions 1 and 2 also has different velocities at these positions.

Problem #1: A garden hose has an unobstructed opening with a cross-sectional area of 2.85 x 10-4 m2, from which water fills a bucket in 30.0 s. The volume of the bucket is 8.00 x 10-3 m3 (about two gallons). Find the speed of the water that leaves the hose through (a) the unobstructed opening and (b) an obstructed opening with half as much area.

Problem #2: In the condition known as atherosclerosis, a deposit, or atheroma, forms on the arterial wall and reduces the opening through which blood can flow. In the carotid artery in the neck, blood flows three times faster through a partially blocked region than it does through an unobstructed region. Determine the ratio of the effective radii of the artery at the two places.