w2 example 1 answers
TRANSCRIPT
1a Write an equation that can be used to work out the
volume of water entering the basin without knowing the
volume of water leaving the basin.
1a • Substitute V2 in the second equation with its equivalent from the first
equation:
1a • Substitute V2 in the second equation with its equivalent from the first
equation:
V1S1 = (V1 +W)S2
1a • Substitute V2 in the second equation with its equivalent from the first
equation:
V1S1 = (V1 +W)S2
• Then rearrange for V1:
1a • Substitute V2 in the second equation with its equivalent from the first
equation:
V1S1 = (V1 +W)S2
• Then rearrange for V1:
V1S1 = V1S2 +WS2
1a • Substitute V2 in the second equation with its equivalent from the first
equation:
V1S1 = (V1 +W)S2
• Then rearrange for V1:
V1S1 = V1S2 +WS2
V1S1 − V1S2 = WS2
1a • Substitute V2 in the second equation with its equivalent from the first
equation:
V1S1 = (V1 +W)S2
• Then rearrange for V1:
V1S1 = V1S2 +WS2
V1S1 − V1S2 = WS2
V1 S1 − S2 = WS2
1a • Substitute V2 in the second equation with its equivalent from the first
equation:
V1S1 = (V1 +W)S2
• Then rearrange for V1:
V1S1 = V1S2 +WS2
V1S1 − V1S2 = WS2
V1 S1 − S2 = WS2
𝐕𝟏 =𝐖𝐒𝟐
𝐒𝟏 − 𝐒𝟐
1b It is important to be able to calculate the additions to the
water also without knowing the volume of water leaving
the basin. Write an equation to do this.
1b • Rearrange your previous equation to make W the subject:
1b • Rearrange your previous equation to make W the subject:
V1 =WS2
S1 − S2
1b • Rearrange your previous equation to make W the subject:
V1 =WS2
S1 − S2
V1 S1 − S2 = WS2
1b • Rearrange your previous equation to make W the subject:
V1 =WS2
S1 − S2
V1 S1 − S2 = WS2
𝐕𝟏 𝐒𝟏 − 𝐒𝟐𝐒𝟐
= 𝐖
1c Over a year, a lagoon of surface area 50m2 gains 1.12m
of water by precipitation and 0.81m by run-off, but loses
1.26m by evaporation. What is W for the lake in m3s-1?
1c • To convert m/year into m3s-1, you need to multiply it by the area if the
basin and divide by the number of seconds in a year:
1c • To convert m/year into m3s-1, you need to multiply it by the area if the
basin and divide by the number of seconds in a year:
1 year = 356 x 24 x 60 x 60 seconds = 31536000s
1c • To convert m/year into m3s-1, you need to multiply it by the area if the
basin and divide by the number of seconds in a year:
1 year = 356 x 24 x 60 x 60 seconds = 31536000s
P = 1.12my−1 =1.12 x 50
31536000= 1.78 x 10−6m3s−1
1c • To convert m/year into m3s-1, you need to multiply it by the area if the
basin and divide by the number of seconds in a year:
1 year = 356 x 24 x 60 x 60 seconds = 31536000s
P = 1.12my−1 =1.12 x 50
31536000= 1.78 x 10−6m3s−1
R = 0.81my−1 =0.81 x 50
31536000= 1.28 x 10−6m3s−1
1c • To convert m/year into m3s-1, you need to multiply it by the area if the
basin and divide by the number of seconds in a year:
1 year = 356 x 24 x 60 x 60 seconds = 31536000s
P = 1.12my−1 =1.12 x 50
31536000= 1.78 x 10−6m3s−1
R = 0.81my−1 =0.81 x 50
31536000= 1.28 x 10−6m3s−1
E = 1.26my−1 =1.26 x 50
31536000= 2.00 x 10−6m3s−1
1c • To convert m/year into m3s-1, you need to multiply it by the area if the
basin and divide by the number of seconds in a year:
1 year = 356 x 24 x 60 x 60 seconds = 31536000s
P = 1.12my−1 =1.12 x 50
31536000= 1.78 x 10−6m3s−1
R = 0.81my−1 =0.81 x 50
31536000= 1.28 x 10−6m3s−1
E = 1.26my−1 =1.26 x 50
31536000= 2.00 x 10−6m3s−1
• Put the converted P, R and E back into the equation for W:
1c • To convert m/year into m3s-1, you need to multiply it by the area if the
basin and divide by the number of seconds in a year:
1 year = 356 x 24 x 60 x 60 seconds = 31536000s
P = 1.12my−1 =1.12 x 50
31536000= 1.78 x 10−6m3s−1
R = 0.81my−1 =0.81 x 50
31536000= 1.28 x 10−6m3s−1
E = 1.26my−1 =1.26 x 50
31536000= 2.00 x 10−6m3s−1
• Put the converted P, R and E back into the equation for W:
W = 1.78 + 1.28 − 2 x 106m3s−1 = 𝟏. 𝟎𝟔 𝐱 𝟏𝟎−𝟔𝐦𝟑𝐬−𝟏
1d Seawater of salinity 35 seeps into the lagoon at a rate of
5.4 x 10-5m3s-1 which has a salinity of exactly 35. What
will the salinity of the lagoon be after at least a year?
1d • Substitute V2 in the second equation with its equivalent from
the first equation:
1d • Substitute V2 in the second equation with its equivalent from
the first equation:
V1S1 = (V1 +W)S2
1d • Substitute V2 in the second equation with its equivalent from
the first equation:
V1S1 = (V1 +W)S2
• Rearrange for S2 and substitute in the values you know:
1d • Substitute V2 in the second equation with its equivalent from
the first equation:
V1S1 = (V1 +W)S2
• Rearrange for S2 and substitute in the values you know:
V1S1(V1 +W)
= S2
1d • Substitute V2 in the second equation with its equivalent from
the first equation:
V1S1 = (V1 +W)S2
• Rearrange for S2 and substitute in the values you know:
V1S1(V1 +W)
= S2
S2 =5.4 x 10−5 x 35
5.4 x 10−5 + 1.06 x 10−6= 𝟑𝟒. 𝟑𝟑