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9 Fluid Dynamics
Calling h A − h B = h
(2)
v =
2gh
(3)
Using simple kinematics, the range
R = vt =
2gh
2(H − h)
g
R = 2
h(H − h)
(4)
(b) In (4) R is unchanged if we replace h by H − h. Therefore, the second
hole must be punched at a depth H − h to get the same range.
9.18 From prob. (9.17)
R = 2
h(H − h)
(1)
Maximum range is obtained by setting dR/dh = 0 and holding H as constant.
This gives h = H/2 and substituting this value in (1), we get R max = H .
9.19 For the water level to remain stationary volume efflux = rate of filling = x
v A =
2gh
A = x = 70 cm
3
/s
h =
x 2
2g A 2 =
(70) 2
2 × 980 × (0.25) 2 = 40 cm
9.20 Let the water level be at a height x at any instant. The efflux velocity will be
v =
√
2gx. As the water flows out, the level of water comes down, Fig. 9.8.
Fig. 9.8
9 Fluid Dynamics
Calling h A − h B = h
(2)
v =
2gh
(3)
Using simple kinematics, the range
R = vt =
2gh
2(H − h)
g
R = 2
h(H − h)
(4)
(b) In (4) R is unchanged if we replace h by H − h. Therefore, the second
hole must be punched at a depth H − h to get the same range.
9.18 From prob. (9.17)
R = 2
h(H − h)
(1)
Maximum range is obtained by setting dR/dh = 0 and holding H as constant.
This gives h = H/2 and substituting this value in (1), we get R max = H .
9.19 For the water level to remain stationary volume efflux = rate of filling = x
v A =
2gh
A = x = 70 cm
3
/s
h =
x 2
2g A 2 =
(70) 2
2 × 980 × (0.25) 2 = 40 cm
9.20 Let the water level be at a height x at any instant. The efflux velocity will be
v =
√
2gx. As the water flows out, the level of water comes down, Fig. 9.8.
Fig. 9.8