EngineeringPushan · Class 9-10
Baandh par paani ka dhakka: trikon dabaav aur ½ρgH²
Kabhi socha hai? Agar baandh ki jheel 20 m se 40 m gehri ho jaaye, toh deewar par dhakka doguna hoga ya usse bhi zyada? Ek engineer ke liye is sawaal ka galat jawab bahut mehnga pad sakta hai.
Socho pehle… phir dekho jawab
Dhakka chaar guna ho jaata hai! Dabaav gehrai ke saath seedha badhta hai (p = ρgh), aur woh poori oonchai H par lagta hai. Kul bal = ausat dabaav × area = (ρgH/2) × H = ½ρgH² (har metre chaudai par). H doguna, toh bal chaar guna.
Dabaav ka chitra: satah par 0, tali par ρgH — deewar par dabaav ek trikon (triangle) ki tarah failta hai. Kul bal = trikon ka area = ½ × ρgH × H = ½ρgH² per metre chaudai. Yeh bal tali se H/3 oonchai par lagta hai (trikon ka kendra).
Udaharan: H = 20 m, ρ = 1000 kg/m³, g ≈ 9.8 m/s²: F ≈ ½ × 1000 × 9.8 × 400 ≈ 19.6 lakh N har metre chaudai par. H = 40 m par ≈ 78.4 lakh N — chaar guna.
Isliye gravity dam ka katav tikona: jahan dabaav zyada (neeche), wahan chaudai aur wazan zyada, jo deewar ko khisakne aur ulatne se rokta hai. Neeche se risaav ka 'uplift' (upar dhakelta paani) deewar ka wazan ghata deta hai, isliye drainage gallery aur pardaa-grouting.
Spillway aur gate kyun: jheel ka star thoda bhi upar gaya toh bal H² ke hisaab se badhta hai — isliye star ki nigraani aur samay par paani chhodna design ka hissa hai. Kadi: star badha, phir H² badha, phir bal tezi se badha, isliye engineer khatre ki line se pehle hi gate kholte hain.
Humne kya kiya :- p = ρgh se deewar par kul bal ½ρgH² nikaala aur uska asar deewar ki shape par dekha.
Isse kya hua :- Samjhe ki gehrai doguni hone par dhakka chaar guna hota hai, isliye baandh tikona aur star ki nigraani zaroori.
Ghar pe try karo
Graph paper par H = 10, 20, 30, 40 m ke liye ½ρgH² ka table banao (ρ = 1000, g = 9.8) aur graph khencho. Phir ek gilaas mein paani bhar kar uski deewar par tape se 0, ½ aur poori oonchai par nishaan lagao aur socho: kis nishaan par dabaav sabse zyada?
Wow!
Jheel ka star sirf 10% badhe toh deewar par kul dhakka lagbhag 21% badh jaata hai — H² ka khel!
3 sawaal
- Baandh par paani ka kul bal (per metre chaudai) kis formula se nikalta hai?
Jawab dekho
½ρgH². Dabaav 0 se ρgH tak trikon ki tarah; area = ½ × ρgH × H = ½ρgH².
- Jheel ki gehrai doguni ho jaaye toh deewar par kul bal kitna ho jaata hai?
Jawab dekho
Chaar guna. Bal H² ke anupaat mein hai, isliye H doguna toh bal chaar guna.
- Baandh par paani ka kul bal tali se kitni oonchai par lagta hai?
Jawab dekho
H/3. Trikon dabaav ka kendra tali se H/3 oonchai par hota hai.
NCERT se jodo: NCERT Class 9 Science — thrust aur pressure; Class 10 Geography — jal sansaadhan aur bahuuddeshiya pariyojanaayein (idea in words)