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Q11PE

Expert-verifiedFound in: Page 428

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**(a) What is the fluid speed in a fire hose with a 9.00-cm diameter carrying 80.0 L of water per second? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if salt water replaced the fresh water in the fire hose?**

**(a) The speed of fluid is \({\bf{12}}{\bf{.6}}\;{\bf{m/s}}\).**

**(b) The flow rate in cubic meter per second is \({\bf{8 \times 1}}{{\bf{0}}^{{\bf{ - 2}}}}\;{{\bf{m}}^{\bf{3}}}{\bf{/s}}\).**

**(c) The answer for flow rate of salt water would not change.**

**(a)**

**Given Data:**

**The diameter of fire hose is \(d = 9\;{\rm{cm}} = 0.09\;{\rm{m}}\)**

**The flow rate of water is \(Q = 80\;{\rm{L/s}}\)**

**The flow rate of blood is \(Q = 3.80 \times {10^9}\;{\rm{c}}{{\rm{m}}^3}/{\rm{s}}\)**

**The flow rate of blood is found by using the formula for flow rate which is equal to product of cross sectional area and speed of blood.**

**The speed of fluid is given as:**

**\(v = \frac{{4Q}}{{\pi {d^2}}}\)**

**Here, \(v\) is the speed of blood flow**

**\(\begin{aligned}v &= \frac{{4\left( {80\;{\rm{L}}/{\rm{s}}} \right)\left( {\frac{{1\;{{\rm{m}}^3}}}{{1000\;{\rm{L}}}}} \right)}}{{\pi {{\left( {0.09\;{\rm{m}}} \right)}^2}}}\\v &= 12.6\;{\rm{m}}/{\rm{s}}\end{aligned}\)**

**Therefore, the speed of fluidis \(12.6\;{\rm{m}}/{\rm{s}}\)**.

**The flow rate in cubic meter per second is given as:**

**\(\begin{aligned}Q &= \left( {80\;{\rm{L}}/{\rm{s}}} \right)\left( {\frac{{1\;{{\rm{m}}^3}}}{{{{10}^3}\;{\rm{L}}}}} \right)\\Q &= 8 \times {10^{ - 2}}\;{{\rm{m}}^3}/{\rm{s}}\end{aligned}\)**

**Therefore, the flow rate in cubic meter per second is \(8 \times {10^{ - 2}}\;{{\rm{m}}^3}/{\rm{s}}\).**

**(c)**

**The flow rate of fluid is independent from the density of fluid so the flow rate for salt water in fire hose remains same.**

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