Velocity of Water in 5 cm Tube: Solve Equation

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To find the velocity of water in a 5 cm radius tube with a flow rate of 10 liters/min, the flow rate must be converted to consistent units. The conversion involves changing liters to milliliters and minutes to seconds, resulting in a flow rate of 166.67 mL/s. The area of the tube is calculated using the formula for the area of a circle, A = πr², yielding an area of approximately 78.54 cm². Using the equation for flow rate (Q = Velocity x Area), the velocity can be determined. Proper unit conversions are essential for accurate calculations in fluid dynamics.
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1.A tube of radius 5 cm is connected to tube of radius 1 cm. Water is forced through the tube at a rate of 10 liters/min. The pressure in the 5 cm tube is 1×10^5 Pa. The density of water is 1000 kg/m3. Assume that the water is nonviscous and uncompressible.
What is the velocity of the water in the 5 cm radius tube?

2. Flow rate of liquid = Velocity X Area.
3. I believe the units are messing me up. I am not sure about the 10 liters/min. but my equation: 10 liters/min = (1000)x(5^2)(∏)(V) I am not coming up with the correct answers, and don't know if this is even close to the right equation. can somone point me in the right direction?
 
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The volume and area need to have the same length units.
 
convert the Liters into milliliters (L-mL) and use the conversion 1mL=1cm^3 than change minutes into seconds (1min=60sec)
 

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