Question

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3.   How high a building could fire hoses effectively spray from the ground?  Fire hose  pressures are around 1 MPa. (It is also said that larger fire engine mounted pumps can deliver from 90-300 gallons per minute, and hoses can be as wide as 30 cm diameter  What alternative estimate would that info give you?)

4.  Butterflies and moths use their slender probosci to sip nectar, plant sap, etc.     Let the radius be 30 μm, and the length be 1.4 mm.   The visocsity varies with the sweetness of the nectar, but you can take it as around 2 mPa-s.   How fast would you predict these lepidoptera can pull in their food?    (Think about the Pressure difference, which we haven't said anything about.)    How does this compare with measured rates of flow of around 3 x 10^-10  m³/s?  The difference turns out to suggest interesting different biology.  

5.  Capillaries are  typically smaller than blood cells--about 5 μm in  diameter.   The pressure difference  across the capillary is  0.7 kPa (measured for hamster skin) .    If  capillaries are ~1 mm long, how fast does the  blood flow through, assuming it has the viscosity of water?    How long  therefore is a red cell in a typical capillary?

Answer 1

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By Bemoulli's principle

\(P_{1}+\frac{p u u}{2}+\rho g h=P_{2}+\frac{p v v}{2}+\rho g H\)

Same velocity

\(\begin{aligned} P_{1} &=P_{2}+\rho g H \\ H &=\frac{P_{1}-P_{2}}{\rho g} \\ & P_{1}-\text { hose pressure } \\ & P_{2}-\text { atmospheric pressure } \\ H &=\frac{1 \times 10^{6}-1.01 \times 10^{5}}{1000 \times 9.8} \\ &=91.73 \\ & H=91.73 \mathrm{~m} \end{aligned}\)

Fire can go height upto \(\mathrm{H}=91.73 \mathrm{~m}\)