Problem 15.57 A river narrows at a rapids from a width of 12m to a width of only
ID: 1314212 • Letter: P
Question
Problem 15.57
A river narrows at a rapids from a width of 12m to a width of only 5.7m . The depth of the river before the rapids is 2.5m ; the depth in the rapids is 0.90m .
Part A
Find the speed of water flowing in the rapids, given that its speed before the rapids is 1.1m/s . Assume the river has a rectangular cross section.
Express your answer using two significant figures.
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Problem 15.57
A river narrows at a rapids from a width of 12m to a width of only 5.7m . The depth of the river before the rapids is 2.5m ; the depth in the rapids is 0.90m .
Part A
Find the speed of water flowing in the rapids, given that its speed before the rapids is 1.1m/s . Assume the river has a rectangular cross section.
Express your answer using two significant figures.
v = m/sSubmitMy AnswersGive Up
Explanation / Answer
m= mass flow rate
p = density
A= area
v= velocity
state 1: water entering control volume
state 2: water leaving control volume
draw a diagram and set up a control volume since no mass is lost in this process the mass entering must equal the mass exiting the system so
m1 = m2
p1A1V1=p2A2v2
assuming density is the same
a1v1=a2v2
v2 = a1v1/a2
a1 = 12* 2.5=30 m^2
a2 = 5.7*0.90=5.13 m^2
v1 =1.1 m/s
v2 =6.4327 m/s